Templated probability distributions. More...

Classes
struct	include_summand
	Template metaprogram to calculate whether a summand needs to be included in a proportional (log) probability calculation. More...

class	welford_covar_estimator

class	welford_var_estimator

Functions
template<bool propto, typename T_y , typename T_loc , typename T_scale >
boost::enable_if_c < contains_fvar< T_y, T_loc, T_scale >::value, typename return_type< T_y, T_loc, T_scale >::type >::type	normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T >
void	autocorrelation (const std::vector< T > &y, std::vector< T > &ac, Eigen::FFT< T > &fft)
	Write autocorrelation estimates for every lag for the specified input sequence into the specified result using the specified FFT engine. More...

template<typename T >
void	autocorrelation (const std::vector< T > &y, std::vector< T > &ac)
	Write autocorrelation estimates for every lag for the specified input sequence into the specified result. More...

template<typename T >
void	autocovariance (const std::vector< T > &y, std::vector< T > &acov, Eigen::FFT< T > &fft)
	Write autocovariance estimates for every lag for the specified input sequence into the specified result using the specified FFT engine. More...

template<typename T >
void	autocovariance (const std::vector< T > &y, std::vector< T > &acov)
	Write autocovariance estimates for every lag for the specified input sequence into the specified result. More...

template<bool propto, typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args < T_prob, T_prior_sample_size > ::type	dirichlet_log (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha)
	The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha. More...

template<typename T_prob , typename T_prior_sample_size >
boost::math::tools::promote_args < T_prob, T_prior_sample_size > ::type	dirichlet_log (const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta, const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &alpha)

template<class RNG >
Eigen::VectorXd	dirichlet_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &alpha, RNG &rng)

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type > ::type	gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
	The log of a Gaussian dynamic linear model (GDLM). More...

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type > ::type	gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type > ::type	gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)
	The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances. More...

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >
return_type< T_y, typename return_type< T_F, T_G, T_V, T_W, T_m0, T_C0 >::type > ::type	gaussian_dlm_obs_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &F, const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &G, const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &V, const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &W, const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &m0, const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &C0)

template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args < T_y, T_dof, T_scale >::type	inv_wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
	The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix. More...

template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args < T_y, T_dof, T_scale >::type	inv_wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)

template<class RNG >
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	inv_wishart_rng (const double nu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng)

template<typename T_shape >
T_shape	do_lkj_constant (const T_shape &eta, const unsigned int &K)

template<bool propto, typename T_covar , typename T_shape >
boost::math::tools::promote_args < T_covar, T_shape >::type	lkj_corr_cholesky_log (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta)

template<typename T_covar , typename T_shape >
boost::math::tools::promote_args < T_covar, T_shape >::type	lkj_corr_cholesky_log (const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const T_shape &eta)

template<bool propto, typename T_y , typename T_shape >
boost::math::tools::promote_args < T_y, T_shape >::type	lkj_corr_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta)

template<typename T_y , typename T_shape >
boost::math::tools::promote_args < T_y, T_shape >::type	lkj_corr_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_shape &eta)

template<class RNG >
Eigen::MatrixXd	lkj_corr_cholesky_rng (const size_t K, const double eta, RNG &rng)

template<class RNG >
Eigen::MatrixXd	lkj_corr_rng (const size_t K, const double eta, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args < T_y, T_loc, T_scale, T_shape > ::type	lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args < T_y, T_loc, T_scale, T_shape > ::type	lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &sigma, const T_shape &eta)

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args < T_y, T_loc, T_scale, T_shape > ::type	lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
boost::math::tools::promote_args < T_y, T_loc, T_scale, T_shape > ::type	lkj_cov_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const T_loc &mu, const T_scale &sigma, const T_shape &eta)

template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args < T_y, T_Mu, T_Sigma, T_D > ::type	matrix_normal_prec_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D)
	The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices. More...

template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D >
boost::math::tools::promote_args < T_y, T_Mu, T_Sigma, T_D > ::type	matrix_normal_prec_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &Mu, const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &D)

template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args < T_y, T_covar, T_w >::type	multi_gp_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
	The log of a multivariate Gaussian Process for the given y, Sigma, and w. More...

template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args < T_y, T_covar, T_w >::type	multi_gp_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)

template<bool propto, typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args < T_y, T_covar, T_w >::type	multi_gp_cholesky_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)
	The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma. More...

template<typename T_y , typename T_covar , typename T_w >
boost::math::tools::promote_args < T_y, T_covar, T_w >::type	multi_gp_cholesky_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &y, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L, const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &w)

template<bool propto, typename T_y , typename T_loc , typename T_covar >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, typename scalar_type < T_loc >::type, T_covar > ::type	multi_normal_log (const T_y &y, const T_loc &mu, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma)

template<typename T_y , typename T_loc , typename T_covar >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, typename scalar_type < T_loc >::type, T_covar > ::type	multi_normal_log (const T_y &y, const T_loc &mu, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma)

template<class RNG >
Eigen::VectorXd	multi_normal_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_covar >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, typename scalar_type < T_loc >::type, T_covar > ::type	multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L)
	The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix. More...

template<typename T_y , typename T_loc , typename T_covar >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, typename scalar_type < T_loc >::type, T_covar > ::type	multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &L)

template<class RNG >
Eigen::VectorXd	multi_normal_cholesky_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_covar >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, typename scalar_type < T_loc >::type, T_covar > ::type	multi_normal_prec_log (const T_y &y, const T_loc &mu, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma)

template<typename T_y , typename T_loc , typename T_covar >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, typename scalar_type < T_loc >::type, T_covar > ::type	multi_normal_prec_log (const T_y &y, const T_loc &mu, const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &Sigma)

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, T_dof, typename scalar_type< T_loc >::type, T_scale >::type	multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &Sigma)
	Return the log of the multivariate Student t distribution at the specified arguments. More...

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
boost::math::tools::promote_args < typename scalar_type< T_y > ::type, T_dof, typename scalar_type< T_loc >::type, T_scale >::type	multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &Sigma)

template<class RNG >
Eigen::VectorXd	multi_student_t_rng (const double nu, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &s, RNG &rng)

template<bool propto, typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args < T_y, T_dof, T_scale >::type	wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)
	The log of the Wishart density for the given W, degrees of freedom, and scale matrix. More...

template<typename T_y , typename T_dof , typename T_scale >
boost::math::tools::promote_args < T_y, T_dof, T_scale >::type	wishart_log (const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &W, const T_dof &nu, const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &S)

template<class RNG >
Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	wishart_rng (const double nu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng)

template<bool propto, typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)

template<typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_log (const typename math::index_type< Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > >::type n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)

template<bool propto, typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)

template<typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)

template<class RNG >
int	categorical_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &theta, RNG &rng)

template<bool propto, typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_logit_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)

template<typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_logit_log (int n, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)

template<bool propto, typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_logit_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)

template<typename T_prob >
boost::math::tools::promote_args < T_prob >::type	categorical_logit_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &beta)

template<bool propto, typename T_prob >
boost::math::tools::promote_args < T_prob >::type	multinomial_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)

template<typename T_prob >
boost::math::tools::promote_args < T_prob >::type	multinomial_log (const std::vector< int > &ns, const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &theta)

template<class RNG >
std::vector< int >	multinomial_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &theta, const int N, RNG &rng)

template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type	beta_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
	The log of the beta density for the specified scalar(s) given the specified sample size(s). More...

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type	beta_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type	beta_cdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)
	Calculates the beta cumulative distribution function for the given variate and scale variables. More...

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type	beta_cdf_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)

template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type< T_y, T_scale_succ, T_scale_fail >::type	beta_ccdf_log (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta)

template<class RNG >
double	beta_rng (const double alpha, const double beta, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	cauchy_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
	The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s). More...

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	cauchy_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	cauchy_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Calculates the cauchy cumulative distribution function for the given variate, location, and scale. More...

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	cauchy_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	cauchy_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<class RNG >
double	cauchy_rng (const double mu, const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	chi_square_log (const T_y &y, const T_dof &nu)
	The log of a chi-squared density for y with the specified degrees of freedom parameter. More...

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	chi_square_log (const T_y &y, const T_dof &nu)

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	chi_square_cdf (const T_y &y, const T_dof &nu)
	Calculates the chi square cumulative distribution function for the given variate and degrees of freedom. More...

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	chi_square_cdf_log (const T_y &y, const T_dof &nu)

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	chi_square_ccdf_log (const T_y &y, const T_dof &nu)

template<class RNG >
double	chi_square_rng (const double nu, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	double_exponential_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	double_exponential_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	double_exponential_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Calculates the double exponential cumulative density function. More...

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	double_exponential_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	double_exponential_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<class RNG >
double	double_exponential_rng (const double mu, const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type	exp_mod_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type	exp_mod_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type	exp_mod_normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type	exp_mod_normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type< T_y, T_loc, T_scale, T_inv_scale >::type	exp_mod_normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda)

template<class RNG >
double	exp_mod_normal_rng (const double mu, const double sigma, const double lambda, RNG &rng)

template<bool propto, typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale > ::type	exponential_log (const T_y &y, const T_inv_scale &beta)
	The log of an exponential density for y with the specified inverse scale parameter. More...

template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale > ::type	exponential_log (const T_y &y, const T_inv_scale &beta)

template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale > ::type	exponential_cdf (const T_y &y, const T_inv_scale &beta)
	Calculates the exponential cumulative distribution function for the given y and beta. More...

template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale > ::type	exponential_cdf_log (const T_y &y, const T_inv_scale &beta)

template<typename T_y , typename T_inv_scale >
return_type< T_y, T_inv_scale > ::type	exponential_ccdf_log (const T_y &y, const T_inv_scale &beta)

template<class RNG >
double	exponential_rng (const double beta, RNG &rng)

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	frechet_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	frechet_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	frechet_cdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	frechet_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	frechet_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<class RNG >
double	frechet_rng (const double alpha, const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type	gamma_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
	The log of a gamma density for y with the specified shape and inverse scale parameters. More...

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type	gamma_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type	gamma_cdf (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
	The cumulative density function for a gamma distribution for y with the specified shape and inverse scale parameters. More...

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type	gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)

template<typename T_y , typename T_shape , typename T_inv_scale >
return_type< T_y, T_shape, T_inv_scale >::type	gamma_ccdf_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)

template<class RNG >
double	gamma_rng (const double alpha, const double beta, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	gumbel_log (const T_y &y, const T_loc &mu, const T_scale &beta)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	gumbel_log (const T_y &y, const T_loc &mu, const T_scale &beta)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	gumbel_cdf (const T_y &y, const T_loc &mu, const T_scale &beta)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	gumbel_cdf_log (const T_y &y, const T_loc &mu, const T_scale &beta)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	gumbel_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &beta)

template<class RNG >
double	gumbel_rng (const double mu, const double beta, RNG &rng)

template<bool propto, typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	inv_chi_square_log (const T_y &y, const T_dof &nu)
	The log of an inverse chi-squared density for y with the specified degrees of freedom parameter. More...

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	inv_chi_square_log (const T_y &y, const T_dof &nu)

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	inv_chi_square_cdf (const T_y &y, const T_dof &nu)

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	inv_chi_square_cdf_log (const T_y &y, const T_dof &nu)

template<typename T_y , typename T_dof >
return_type< T_y, T_dof >::type	inv_chi_square_ccdf_log (const T_y &y, const T_dof &nu)

template<class RNG >
double	inv_chi_square_rng (const double nu, RNG &rng)

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	inv_gamma_log (const T_y &y, const T_shape &alpha, const T_scale &beta)
	The log of an inverse gamma density for y with the specified shape and scale parameters. More...

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	inv_gamma_log (const T_y &y, const T_shape &alpha, const T_scale &beta)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	inv_gamma_cdf (const T_y &y, const T_shape &alpha, const T_scale &beta)
	The CDF of an inverse gamma density for y with the specified shape and scale parameters. More...

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	inv_gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &beta)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	inv_gamma_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &beta)

template<class RNG >
double	inv_gamma_rng (const double alpha, const double beta, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	logistic_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	logistic_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	logistic_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	logistic_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	logistic_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<class RNG >
double	logistic_rng (const double mu, const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	lognormal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	lognormal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	lognormal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	lognormal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	lognormal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<class RNG >
double	lognormal_rng (const double mu, const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale >
boost::enable_if_c < is_var_or_arithmetic< T_y, T_loc, T_scale >::value, typename return_type< T_y, T_loc, T_scale >::type >::type	normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
	The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s). More...

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Calculates the normal cumulative distribution function for the given variate, location, and scale. More...

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)

template<class RNG >
double	normal_rng (const double mu, const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type	pareto_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)

template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type	pareto_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)

template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type	pareto_cdf (const T_y &y, const T_scale &y_min, const T_shape &alpha)

template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type	pareto_cdf_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)

template<typename T_y , typename T_scale , typename T_shape >
return_type< T_y, T_scale, T_shape >::type	pareto_ccdf_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)

template<class RNG >
double	pareto_rng (const double y_min, const double alpha, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	pareto_type_2_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	pareto_type_2_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	pareto_type_2_cdf (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	pareto_type_2_cdf_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	pareto_type_2_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)

template<class RNG >
double	pareto_type_2_rng (const double mu, const double lambda, const double alpha, RNG &rng)

template<bool propto, typename T_y , typename T_scale >
return_type< T_y, T_scale >::type	rayleigh_log (const T_y &y, const T_scale &sigma)

template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type	rayleigh_log (const T_y &y, const T_scale &sigma)

template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type	rayleigh_cdf (const T_y &y, const T_scale &sigma)

template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type	rayleigh_cdf_log (const T_y &y, const T_scale &sigma)

template<typename T_y , typename T_scale >
return_type< T_y, T_scale >::type	rayleigh_ccdf_log (const T_y &y, const T_scale &sigma)

template<class RNG >
double	rayleigh_rng (const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type	scaled_inv_chi_square_log (const T_y &y, const T_dof &nu, const T_scale &s)
	The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter. More...

template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type	scaled_inv_chi_square_log (const T_y &y, const T_dof &nu, const T_scale &s)

template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type	scaled_inv_chi_square_cdf (const T_y &y, const T_dof &nu, const T_scale &s)
	The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter. More...

template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type	scaled_inv_chi_square_cdf_log (const T_y &y, const T_dof &nu, const T_scale &s)

template<typename T_y , typename T_dof , typename T_scale >
return_type< T_y, T_dof, T_scale >::type	scaled_inv_chi_square_ccdf_log (const T_y &y, const T_dof &nu, const T_scale &s)

template<class RNG >
double	scaled_inv_chi_square_rng (const double nu, const double s, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	skew_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	skew_normal_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	skew_normal_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	skew_normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type< T_y, T_loc, T_scale, T_shape >::type	skew_normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)

template<class RNG >
double	skew_normal_rng (const double mu, const double sigma, const double alpha, RNG &rng)

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type	student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)
	The log of the Student-t density for the given y, nu, mean, and scale parameter. More...

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type	student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type	student_t_cdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type	student_t_cdf_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type< T_y, T_dof, T_loc, T_scale >::type	student_t_ccdf_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &sigma)

template<class RNG >
double	student_t_rng (const double nu, const double mu, const double sigma, RNG &rng)

template<bool propto, typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type	uniform_log (const T_y &y, const T_low &alpha, const T_high &beta)
	The log of a uniform density for the given y, lower, and upper bound. More...

template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type	uniform_log (const T_y &y, const T_low &alpha, const T_high &beta)

template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type	uniform_cdf (const T_y &y, const T_low &alpha, const T_high &beta)

template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type	uniform_cdf_log (const T_y &y, const T_low &alpha, const T_high &beta)

template<typename T_y , typename T_low , typename T_high >
return_type< T_y, T_low, T_high >::type	uniform_ccdf_log (const T_y &y, const T_low &alpha, const T_high &beta)

template<class RNG >
double	uniform_rng (const double alpha, const double beta, RNG &rng)

template<bool propto, typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	von_mises_log (T_y const &y, T_loc const &mu, T_scale const &kappa)

template<typename T_y , typename T_loc , typename T_scale >
return_type< T_y, T_loc, T_scale >::type	von_mises_log (T_y const &y, T_loc const &mu, T_scale const &kappa)

template<class RNG >
double	von_mises_rng (const double mu, const double kappa, RNG &rng)

template<bool propto, typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	weibull_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	weibull_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	weibull_cdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	weibull_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<typename T_y , typename T_shape , typename T_scale >
return_type< T_y, T_shape, T_scale >::type	weibull_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)

template<class RNG >
double	weibull_rng (const double alpha, const double sigma, RNG &rng)

template<bool propto, typename T_n , typename T_prob >
return_type< T_prob >::type	bernoulli_log (const T_n &n, const T_prob &theta)

template<typename T_y , typename T_prob >
return_type< T_prob >::type	bernoulli_log (const T_y &n, const T_prob &theta)

template<bool propto, typename T_n , typename T_prob >
return_type< T_prob >::type	bernoulli_logit_log (const T_n &n, const T_prob &theta)

template<typename T_n , typename T_prob >
return_type< T_prob >::type	bernoulli_logit_log (const T_n &n, const T_prob &theta)

template<typename T_n , typename T_prob >
return_type< T_prob >::type	bernoulli_cdf (const T_n &n, const T_prob &theta)

template<typename T_n , typename T_prob >
return_type< T_prob >::type	bernoulli_cdf_log (const T_n &n, const T_prob &theta)

template<typename T_n , typename T_prob >
return_type< T_prob >::type	bernoulli_ccdf_log (const T_n &n, const T_prob &theta)

template<class RNG >
int	bernoulli_rng (const double theta, RNG &rng)

template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 > ::type	beta_binomial_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 > ::type	beta_binomial_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 > ::type	beta_binomial_cdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 > ::type	beta_binomial_cdf_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type< T_size1, T_size2 > ::type	beta_binomial_ccdf_log (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)

template<class RNG >
int	beta_binomial_rng (const int N, const double alpha, const double beta, RNG &rng)

template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type	binomial_log (const T_n &n, const T_N &N, const T_prob &theta)

template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type	binomial_log (const T_n &n, const T_N &N, const T_prob &theta)

template<bool propto, typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type	binomial_logit_log (const T_n &n, const T_N &N, const T_prob &alpha)

template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type	binomial_logit_log (const T_n &n, const T_N &N, const T_prob &alpha)

template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type	binomial_cdf (const T_n &n, const T_N &N, const T_prob &theta)

template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type	binomial_cdf_log (const T_n &n, const T_N &N, const T_prob &theta)

template<typename T_n , typename T_N , typename T_prob >
return_type< T_prob >::type	binomial_ccdf_log (const T_n &n, const T_N &N, const T_prob &theta)

template<class RNG >
int	binomial_rng (const int N, const double theta, RNG &rng)

template<bool propto, typename T_n , typename T_N , typename T_a , typename T_b >
double	hypergeometric_log (const T_n &n, const T_N &N, const T_a &a, const T_b &b)

template<typename T_n , typename T_N , typename T_a , typename T_b >
double	hypergeometric_log (const T_n &n, const T_N &N, const T_a &a, const T_b &b)

template<class RNG >
int	hypergeometric_rng (const int N, const int a, const int b, RNG &rng)

template<bool propto, typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type	neg_binomial_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type	neg_binomial_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type	neg_binomial_cdf (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type	neg_binomial_cdf_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)

template<typename T_n , typename T_shape , typename T_inv_scale >
return_type< T_shape, T_inv_scale >::type	neg_binomial_ccdf_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)

template<class RNG >
int	neg_binomial_rng (const double alpha, const double beta, RNG &rng)

template<bool propto, typename T_n , typename T_location , typename T_inv_scale >
return_type< T_location, T_inv_scale >::type	neg_binomial_2_log (const T_n &n, const T_location &mu, const T_inv_scale &phi)

template<typename T_n , typename T_location , typename T_inv_scale >
return_type< T_location, T_inv_scale >::type	neg_binomial_2_log (const T_n &n, const T_location &mu, const T_inv_scale &phi)

template<bool propto, typename T_n , typename T_log_location , typename T_inv_scale >
return_type< T_log_location, T_inv_scale >::type	neg_binomial_2_log_log (const T_n &n, const T_log_location &eta, const T_inv_scale &phi)

template<typename T_n , typename T_log_location , typename T_inv_scale >
return_type< T_log_location, T_inv_scale >::type	neg_binomial_2_log_log (const T_n &n, const T_log_location &eta, const T_inv_scale &phi)

template<class RNG >
int	neg_binomial_2_rng (const double mu, const double phi, RNG &rng)

template<class RNG >
int	neg_binomial_2_log_rng (const double eta, const double phi, RNG &rng)

template<typename T >
T	log_inv_logit_diff (const T &alpha, const T &beta)

template<bool propto, typename T_lambda , typename T_cut >
boost::math::tools::promote_args < T_lambda, T_cut >::type	ordered_logistic_log (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c)
	Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model. More...

template<typename T_lambda , typename T_cut >
boost::math::tools::promote_args < T_lambda, T_cut >::type	ordered_logistic_log (int y, const T_lambda &lambda, const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &c)

template<class RNG >
int	ordered_logistic_rng (const double eta, const Eigen::Matrix< double, Eigen::Dynamic, 1 > &c, RNG &rng)

template<bool propto, typename T_n , typename T_rate >
return_type< T_rate >::type	poisson_log (const T_n &n, const T_rate &lambda)

template<typename T_n , typename T_rate >
return_type< T_rate >::type	poisson_log (const T_n &n, const T_rate &lambda)

template<bool propto, typename T_n , typename T_log_rate >
return_type< T_log_rate >::type	poisson_log_log (const T_n &n, const T_log_rate &alpha)

template<typename T_n , typename T_log_rate >
return_type< T_log_rate >::type	poisson_log_log (const T_n &n, const T_log_rate &alpha)

template<typename T_n , typename T_rate >
return_type< T_rate >::type	poisson_cdf (const T_n &n, const T_rate &lambda)

template<typename T_n , typename T_rate >
return_type< T_rate >::type	poisson_cdf_log (const T_n &n, const T_rate &lambda)

template<typename T_n , typename T_rate >
return_type< T_rate >::type	poisson_ccdf_log (const T_n &n, const T_rate &lambda)

template<class RNG >
int	poisson_rng (const double lambda, RNG &rng)

template<typename T >
void	factor_U (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &U, Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs)
	This function is intended to make starting values, given a unit upper-triangular matrix U such that U'DU is a correlation matrix. More...

template<typename T >
bool	factor_cov_matrix (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &Sigma, Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, Eigen::Array< T, Eigen::Dynamic, 1 > &sds)
	This function is intended to make starting values, given a covariance matrix Sigma. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	read_corr_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K)
	Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	read_corr_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K)
	Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	read_corr_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K, T &log_prob)
	Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	read_corr_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const size_t K, T &log_prob)
	Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	read_cov_L (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds, T &log_prob)
	This is the function that should be called prior to evaluating the density of any elliptical distribution. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	read_cov_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds, T &log_prob)
	A generally worse alternative to call prior to evaluating the density of an elliptical distribution. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	read_cov_matrix (const Eigen::Array< T, Eigen::Dynamic, 1 > &CPCs, const Eigen::Array< T, Eigen::Dynamic, 1 > &sds)
	Builds a covariance matrix from CPCs and standard deviations. More...

template<typename T >
const Eigen::Array< T, Eigen::Dynamic, 1 >	make_nu (const T eta, const size_t K)
	This function calculates the degrees of freedom for the t distribution that corresponds to the shape parameter in the Lewandowski et. More...

template<typename T >
T	identity_constrain (T x)
	Returns the result of applying the identity constraint transform to the input. More...

template<typename T >
T	identity_constrain (const T x, T &)
	Returns the result of applying the identity constraint transform to the input and increments the log probability reference with the log absolute Jacobian determinant. More...

template<typename T >
T	identity_free (const T y)
	Returns the result of applying the inverse of the identity constraint transform to the input. More...

template<typename T >
T	positive_constrain (const T x)
	Return the positive value for the specified unconstrained input. More...

template<typename T >
T	positive_constrain (const T x, T &lp)
	Return the positive value for the specified unconstrained input, incrementing the scalar reference with the log absolute Jacobian determinant. More...

template<typename T >
T	positive_free (const T y)
	Return the unconstrained value corresponding to the specified positive-constrained value. More...

template<typename T , typename TL >
T	lb_constrain (const T x, const TL lb)
	Return the lower-bounded value for the specified unconstrained input and specified lower bound. More...

template<typename T , typename TL >
boost::math::tools::promote_args < T, TL >::type	lb_constrain (const T x, const TL lb, T &lp)
	Return the lower-bounded value for the speicifed unconstrained input and specified lower bound, incrementing the specified reference with the log absolute Jacobian determinant of the transform. More...

template<typename T , typename TL >
boost::math::tools::promote_args < T, TL >::type	lb_free (const T y, const TL lb)
	Return the unconstrained value that produces the specified lower-bound constrained value. More...

template<typename T , typename TU >
boost::math::tools::promote_args < T, TU >::type	ub_constrain (const T x, const TU ub)
	Return the upper-bounded value for the specified unconstrained scalar and upper bound. More...

template<typename T , typename TU >
boost::math::tools::promote_args < T, TU >::type	ub_constrain (const T x, const TU ub, T &lp)
	Return the upper-bounded value for the specified unconstrained scalar and upper bound and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...

template<typename T , typename TU >
boost::math::tools::promote_args < T, TU >::type	ub_free (const T y, const TU ub)
	Return the free scalar that corresponds to the specified upper-bounded value with respect to the specified upper bound. More...

template<typename T , typename TL , typename TU >
boost::math::tools::promote_args < T, TL, TU >::type	lub_constrain (const T x, TL lb, TU ub)
	Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds. More...

template<typename T , typename TL , typename TU >
boost::math::tools::promote_args < T, TL, TU >::type	lub_constrain (const T x, const TL lb, const TU ub, T &lp)
	Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds and increment the specified log probability with the log absolute Jacobian determinant. More...

template<typename T , typename TL , typename TU >
boost::math::tools::promote_args < T, TL, TU >::type	lub_free (const T y, TL lb, TU ub)
	Return the unconstrained scalar that transforms to the specified lower- and upper-bounded scalar given the specified bounds. More...

template<typename T >
T	prob_constrain (const T x)
	Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar. More...

template<typename T >
T	prob_constrain (const T x, T &lp)
	Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...

template<typename T >
T	prob_free (const T y)
	Return the free scalar that when transformed to a probability produces the specified scalar. More...

template<typename T >
T	corr_constrain (const T x)
	Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive). More...

template<typename T >
T	corr_constrain (const T x, T &lp)
	Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive). More...

template<typename T >
T	corr_free (const T y)
	Return the unconstrained scalar that when transformed to a valid correlation produces the specified value. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	unit_vector_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y)
	Return the unit length vector corresponding to the free vector y. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	unit_vector_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, T &lp)
	Return the unit length vector corresponding to the free vector y. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	unit_vector_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	simplex_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y)
	Return the simplex corresponding to the specified free vector. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	simplex_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, T &lp)
	Return the simplex corresponding to the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	simplex_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
	Return an unconstrained vector that when transformed produces the specified simplex. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
	Return an increasing ordered vector derived from the specified free vector. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &lp)
	Return a positive valued, increasing ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	ordered_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y)
	Return the vector of unconstrained scalars that transform to the specified positive ordered vector. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	positive_ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x)
	Return an increasing positive ordered vector derived from the specified free vector. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	positive_ordered_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, T &lp)
	Return a positive valued, increasing positive ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	positive_ordered_free (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y)
	Return the vector of unconstrained scalars that transform to the specified positive ordered vector. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cholesky_factor_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int M, int N)
	Return the Cholesky factor of the specified size read from the specified vector. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cholesky_factor_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, int M, int N, T &lp)
	Return the Cholesky factor of the specified size read from the specified vector and increment the specified log probability reference with the log Jacobian adjustment of the transform. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	cholesky_factor_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
	Return the unconstrained vector of parameters correspdonding to the specified Cholesky factor. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cholesky_corr_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, int K)

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cholesky_corr_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &y, int K, T &lp)

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	cholesky_corr_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &x)

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	corr_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type k)
	Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	corr_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type k, T &lp)
	Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	corr_matrix_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
	Return the vector of unconstrained partial correlations that define the specified correlation matrix when transformed. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cov_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type K)
	Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2). More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cov_matrix_constrain (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > >::type K, T &lp)
	Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2). More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	cov_matrix_free (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
	The covariance matrix derived from the symmetric view of the lower-triangular view of the K by K specified matrix is freed to return a vector of size K + (K choose 2). More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cov_matrix_constrain_lkj (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t k)
	Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic >	cov_matrix_constrain_lkj (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &x, size_t k, T &lp)
	Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values and increment the specified log probability reference with the log absolute Jacobian determinant. More...

template<typename T >
Eigen::Matrix< T, Eigen::Dynamic, 1 >	cov_matrix_free_lkj (const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &y)
	Return the vector of unconstrained partial correlations and deviations that transform to the specified covariance matrix. More...

Variables
const double	CONSTRAINT_TOLERANCE = 1E-8

Detailed Description

Templated probability distributions.

All paramaterizations are based on Bayesian Data Analysis. Error handling for the distributions is described in Error Handling Policies.

Function Documentation

template<typename T >

void stan::prob::autocorrelation	(	const std::vector< T > &	y,
		std::vector< T > &	ac,
		Eigen::FFT< T > &	fft
	)

Write autocorrelation estimates for every lag for the specified input sequence into the specified result using the specified FFT engine.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

An FFT engine can be created for reuse for type double with:

    Eigen::FFT<double> fft;

Template Parameters

T	Scalar type.

Parameters

y	Input sequence.
ac	Autocorrelations.
fft	FFT engine instance.

Definition at line 56 of file autocorrelation.hpp.

template<typename T >

void stan::prob::autocorrelation	(	const std::vector< T > &	y,
		std::vector< T > &	ac
	)

Write autocorrelation estimates for every lag for the specified input sequence into the specified result.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

This method is just a light wrapper around the three-argument autocorrelation function

Template Parameters

T	Scalar type.

Parameters

y	Input sequence.
ac	Autocorrelations.

Definition at line 126 of file autocorrelation.hpp.

template<typename T >

void stan::prob::autocovariance	(	const std::vector< T > &	y,
		std::vector< T > &	acov,
		Eigen::FFT< T > &	fft
	)

Write autocovariance estimates for every lag for the specified input sequence into the specified result using the specified FFT engine.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

An FFT engine can be created for reuse for type double with:

    Eigen::FFT<double> fft;

Template Parameters

T	Scalar type.

Parameters

y	Input sequence.
acov	Autocovariance.
fft	FFT engine instance.

Definition at line 33 of file autocovariance.hpp.

template<typename T >

void stan::prob::autocovariance	(	const std::vector< T > &	y,
		std::vector< T > &	acov
	)

Write autocovariance estimates for every lag for the specified input sequence into the specified result.

The return vector be resized to the same length as the input sequence with lags given by array index.

The implementation involves a fast Fourier transform, followed by a normalization, followed by an inverse transform.

This method is just a light wrapper around the three-argument autocovariance function

Template Parameters

T	Scalar type.

Parameters

y	Input sequence.
acov	Autocovariances.

Definition at line 62 of file autocovariance.hpp.

template<typename T_n , typename T_prob >

return_type<T_prob>::type stan::prob::bernoulli_ccdf_log	(	const T_n &	n,
		const T_prob &	theta
	)

Definition at line 333 of file bernoulli.hpp.

template<typename T_n , typename T_prob >

return_type<T_prob>::type stan::prob::bernoulli_cdf	(	const T_n &	n,
		const T_prob &	theta
	)

Definition at line 212 of file bernoulli.hpp.

template<typename T_n , typename T_prob >

return_type<T_prob>::type stan::prob::bernoulli_cdf_log	(	const T_n &	n,
		const T_prob &	theta
	)

Definition at line 274 of file bernoulli.hpp.

template<bool propto, typename T_n , typename T_prob >

return_type<T_prob>::type stan::prob::bernoulli_log	(	const T_n &	n,
		const T_prob &	theta
	)

Definition at line 25 of file bernoulli.hpp.

template<typename T_y , typename T_prob >

return_type<T_prob>::type stan::prob::bernoulli_log	(	const T_y &	n,
		const T_prob &	theta
	)

inline

Definition at line 118 of file bernoulli.hpp.

template<bool propto, typename T_n , typename T_prob >

return_type<T_prob>::type stan::prob::bernoulli_logit_log	(	const T_n &	n,
		const T_prob &	theta
	)

Definition at line 128 of file bernoulli.hpp.

template<typename T_n , typename T_prob >

return_type<T_prob>::type stan::prob::bernoulli_logit_log	(	const T_n &	n,
		const T_prob &	theta
	)

inline

Definition at line 204 of file bernoulli.hpp.

template<class RNG >

int stan::prob::bernoulli_rng	(	const double	theta,
		RNG &	rng
	)

inline

Definition at line 394 of file bernoulli.hpp.

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >

return_type<T_size1,T_size2>::type stan::prob::beta_binomial_ccdf_log	(	const T_n &	n,
		const T_N &	N,
		const T_size1 &	alpha,
		const T_size2 &	beta
	)

Definition at line 428 of file beta_binomial.hpp.

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >

return_type<T_size1,T_size2>::type stan::prob::beta_binomial_cdf	(	const T_n &	n,
		const T_N &	N,
		const T_size1 &	alpha,
		const T_size2 &	beta
	)

Definition at line 191 of file beta_binomial.hpp.

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >

return_type<T_size1,T_size2>::type stan::prob::beta_binomial_cdf_log	(	const T_n &	n,
		const T_N &	N,
		const T_size1 &	alpha,
		const T_size2 &	beta
	)

Definition at line 314 of file beta_binomial.hpp.

template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 >

return_type<T_size1,T_size2>::type stan::prob::beta_binomial_log	(	const T_n &	n,
		const T_N &	N,
		const T_size1 &	alpha,
		const T_size2 &	beta
	)

Definition at line 28 of file beta_binomial.hpp.

template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >

return_type<T_size1,T_size2>::type stan::prob::beta_binomial_log	(	const T_n &	n,
		const T_N &	N,
		const T_size1 &	alpha,
		const T_size2 &	beta
	)

Definition at line 182 of file beta_binomial.hpp.

template<class RNG >

int stan::prob::beta_binomial_rng	(	const int	N,
		const double	alpha,
		const double	beta,
		RNG &	rng
	)

inline

Definition at line 541 of file beta_binomial.hpp.

template<typename T_y , typename T_scale_succ , typename T_scale_fail >

return_type<T_y,T_scale_succ,T_scale_fail>::type stan::prob::beta_ccdf_log	(	const T_y &	y,
		const T_scale_succ &	alpha,
		const T_scale_fail &	beta
	)

Definition at line 476 of file beta.hpp.

template<typename T_y , typename T_scale_succ , typename T_scale_fail >

return_type<T_y,T_scale_succ,T_scale_fail>::type stan::prob::beta_cdf	(	const T_y &	y,
		const T_scale_succ &	alpha,
		const T_scale_fail &	beta
	)

Calculates the beta cumulative distribution function for the given variate and scale variables.

Parameters

y	A scalar variate.
alpha	Prior sample size.
beta	Prior sample size.

Returns: The beta cdf evaluated at the specified arguments.

Template Parameters

T_y	Type of y.
T_scale_succ	Type of alpha.
T_scale_fail	Type of beta.

Definition at line 213 of file beta.hpp.

template<typename T_y , typename T_scale_succ , typename T_scale_fail >

return_type<T_y,T_scale_succ,T_scale_fail>::type stan::prob::beta_cdf_log	(	const T_y &	y,
		const T_scale_succ &	alpha,
		const T_scale_fail &	beta
	)

Definition at line 358 of file beta.hpp.

template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail >

return_type<T_y,T_scale_succ,T_scale_fail>::type stan::prob::beta_log	(	const T_y &	y,
		const T_scale_succ &	alpha,
		const T_scale_fail &	beta
	)

The log of the beta density for the specified scalar(s) given the specified sample size(s).

y, alpha, or beta can each either be scalar or std::vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/alpha/beta triple.

Prior sample sizes, alpha and beta, must be greater than 0.

Parameters

y	(Sequence of) scalar(s).
alpha	(Sequence of) prior sample size(s).
beta	(Sequence of) prior sample size(s).

Returns: The log of the product of densities.

Template Parameters

T_y	Type of scalar outcome.
T_scale_succ	Type of prior scale for successes.
T_scale_fail	Type of prior scale for failures.

Error Policy:

See Error Handling Policies for details. Conditions:

All parameters must not be NaN.
alpha must be positive and finite.
beta must be positive and finite.

Definition at line 46 of file beta.hpp.

template<typename T_y , typename T_scale_succ , typename T_scale_fail >

return_type<T_y,T_scale_succ,T_scale_fail>::type stan::prob::beta_log	(	const T_y &	y,
		const T_scale_succ &	alpha,
		const T_scale_fail &	beta
	)

inline

Definition at line 194 of file beta.hpp.

template<class RNG >

double stan::prob::beta_rng	(	const double	alpha,
		const double	beta,
		RNG &	rng
	)

inline

Definition at line 593 of file beta.hpp.

template<typename T_n , typename T_N , typename T_prob >

return_type<T_prob>::type stan::prob::binomial_ccdf_log	(	const T_n &	n,
		const T_N &	N,
		const T_prob &	theta
	)

Definition at line 399 of file binomial.hpp.

template<typename T_n , typename T_N , typename T_prob >

return_type<T_prob>::type stan::prob::binomial_cdf	(	const T_n &	n,
		const T_N &	N,
		const T_prob &	theta
	)

Definition at line 249 of file binomial.hpp.

template<typename T_n , typename T_N , typename T_prob >

return_type<T_prob>::type stan::prob::binomial_cdf_log	(	const T_n &	n,
		const T_N &	N,
		const T_prob &	theta
	)

Definition at line 329 of file binomial.hpp.

template<bool propto, typename T_n , typename T_N , typename T_prob >

return_type<T_prob>::type stan::prob::binomial_log	(	const T_n &	n,
		const T_N &	N,
		const T_prob &	theta
	)

Definition at line 31 of file binomial.hpp.

template<typename T_n , typename T_N , typename T_prob >

return_type<T_prob>::type stan::prob::binomial_log	(	const T_n &	n,
		const T_N &	N,
		const T_prob &	theta
	)

inline

Definition at line 129 of file binomial.hpp.

template<bool propto, typename T_n , typename T_N , typename T_prob >

return_type<T_prob>::type stan::prob::binomial_logit_log	(	const T_n &	n,
		const T_N &	N,
		const T_prob &	alpha
	)

Definition at line 142 of file binomial.hpp.

template<typename T_n , typename T_N , typename T_prob >

return_type<T_prob>::type stan::prob::binomial_logit_log	(	const T_n &	n,
		const T_N &	N,
		const T_prob &	alpha
	)

inline

Definition at line 239 of file binomial.hpp.

template<class RNG >

int stan::prob::binomial_rng	(	const int	N,
		const double	theta,
		RNG &	rng
	)

inline

Definition at line 470 of file binomial.hpp.

template<bool propto, typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_log	(	int	n,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta
	)

Definition at line 23 of file categorical.hpp.

template<typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_log	(	const typename math::index_type< Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > >::type	n,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta
	)

inline

Definition at line 59 of file categorical.hpp.

template<bool propto, typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_log	(	const std::vector< int > &	ns,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta
	)

Definition at line 72 of file categorical.hpp.

template<typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_log	(	const std::vector< int > &	ns,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta
	)

inline

Definition at line 124 of file categorical.hpp.

template<bool propto, typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_logit_log	(	int	n,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	beta
	)

Definition at line 21 of file categorical_logit.hpp.

template<typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_logit_log	(	int	n,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	beta
	)

inline

Definition at line 46 of file categorical_logit.hpp.

template<bool propto, typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_logit_log	(	const std::vector< int > &	ns,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	beta
	)

Definition at line 54 of file categorical_logit.hpp.

template<typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::categorical_logit_log	(	const std::vector< int > &	ns,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	beta
	)

inline

Definition at line 91 of file categorical_logit.hpp.

template<class RNG >

int stan::prob::categorical_rng	(	const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	theta,
		RNG &	rng
	)

inline

Definition at line 131 of file categorical.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::cauchy_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 322 of file cauchy.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::cauchy_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Calculates the cauchy cumulative distribution function for the given variate, location, and scale.

$\frac{1}{\pi}\arctan\left(\frac{y-\mu}{\sigma}\right) + \frac{1}{2}$

Errors are configured by policy. All variables must be finite and the scale must be strictly greater than zero.

Parameters

y	A scalar variate.
mu	The location parameter.
sigma	The scale parameter.

Returns

Definition at line 158 of file cauchy.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::cauchy_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 255 of file cauchy.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::cauchy_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

The log of the Cauchy density for the specified scalar(s) given the specified location parameter(s) and scale parameter(s).

y, mu, or sigma can each either be scalar or std::vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/mu/sigma triple.

Parameters

y	(Sequence of) scalar(s).
mu	(Sequence of) location(s).
sigma	(Sequence of) scale(s).

Returns: The log of the product of densities.

Template Parameters

T_y	Type of scalar outcome.
T_loc	Type of location.
T_scale	Type of scale.

Error Policy:

See Error Handling Policies for details. Conditions:

All parameters must not be NaN.
sigma must be positive.

Definition at line 42 of file cauchy.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::cauchy_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

inline

Definition at line 136 of file cauchy.hpp.

template<class RNG >

double stan::prob::cauchy_rng	(	const double	mu,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 388 of file cauchy.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::chi_square_ccdf_log	(	const T_y &	y,
		const T_dof &	nu
	)

Definition at line 348 of file chi_square.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::chi_square_cdf	(	const T_y &	y,
		const T_dof &	nu
	)

Calculates the chi square cumulative distribution function for the given variate and degrees of freedom.

y A scalar variate. nu Degrees of freedom.

Returns: The cdf of the chi square distribution

Definition at line 154 of file chi_square.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::chi_square_cdf_log	(	const T_y &	y,
		const T_dof &	nu
	)

Definition at line 254 of file chi_square.hpp.

template<bool propto, typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::chi_square_log	(	const T_y &	y,
		const T_dof &	nu
	)

The log of a chi-squared density for y with the specified degrees of freedom parameter.

The degrees of freedom prarameter must be greater than 0. y must be greater than or equal to 0.

$\begin{eqnarray*} y &\sim& \chi^2_\nu \\ \log (p (y \,|\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)} y^{\nu / 2 - 1} \exp^{- y / 2} \right) \\ &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) + (\frac{\nu}{2} - 1) \log(y) - \frac{y}{2} \\ & & \mathrm{ where } \; y \ge 0 \end{eqnarray*}$

Parameters

y	A scalar variable.
nu	Degrees of freedom.

Exceptions

std::domain_error	if nu is not greater than or equal to 0
std::domain_error	if y is not greater than or equal to 0.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.

Definition at line 43 of file chi_square.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::chi_square_log	(	const T_y &	y,
		const T_dof &	nu
	)

inline

Definition at line 139 of file chi_square.hpp.

template<class RNG >

double stan::prob::chi_square_rng	(	const double	nu,
		RNG &	rng
	)

inline

Definition at line 442 of file chi_square.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cholesky_corr_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	y,
		int	K
	)

Definition at line 1512 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cholesky_corr_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	y,
		int	K,
		T &	lp
	)

Definition at line 1550 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::cholesky_corr_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & x )

Definition at line 1592 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cholesky_factor_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		int	M,
		int	N
	)

Return the Cholesky factor of the specified size read from the specified vector.

A total of (N choose 2) + N + (M - N) * N elements are required to read an M by N Cholesky factor.

Template Parameters

T	Type of scalars in matrix

Parameters

x	Vector of unconstrained values
M	Number of rows
N	Number of columns

Returns: Cholesky factor

Definition at line 1412 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cholesky_factor_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		int	M,
		int	N,
		T &	lp
	)

Return the Cholesky factor of the specified size read from the specified vector and increment the specified log probability reference with the log Jacobian adjustment of the transform.

A total of (N choose 2) + N + N * (M - N) free parameters are required to read an M by N Cholesky factor.

Template Parameters

T	Type of scalars in matrix

Parameters

x	Vector of unconstrained values
M	Number of rows
N	Number of columns
lp	Log probability that is incremented with the log Jacobian

Returns: Cholesky factor

Definition at line 1455 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::cholesky_factor_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & y )

Return the unconstrained vector of parameters correspdonding to the specified Cholesky factor.

A Cholesky factor must be lower triangular and have positive diagonal elements.

Parameters

y	Cholesky factor.

Returns: Unconstrained parameters for Cholesky factor.

Exceptions

std::domain_error If the matrix is not a Cholesky factor.

Definition at line 1485 of file transform.hpp.

template<typename T >

T stan::prob::corr_constrain ( const T x )

inline

Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive).

The transform used is the hyperbolic tangent function,

$f(x) = \tanh x = \frac{\exp(2x) - 1}{\exp(2x) + 1}$ .

Parameters

x	Scalar input.

Returns: Result of transforming the input to fall between -1 and 1.

Template Parameters

T	Type of scalar.

Definition at line 952 of file transform.hpp.

template<typename T >

T stan::prob::corr_constrain	(	const T	x,
		T &	lp
	)

inline

Return the result of transforming the specified scalar to have a valid correlation value between -1 and 1 (inclusive).

The transform used is as specified for corr_constrain(T). The log absolute Jacobian determinant is

$\log | \frac{d}{dx} \tanh x | = \log (1 - \tanh^2 x)$ .

Template Parameters

T	Type of scalar.

Definition at line 970 of file transform.hpp.

template<typename T >

T stan::prob::corr_free ( const T y )

inline

Return the unconstrained scalar that when transformed to a valid correlation produces the specified value.

This function inverts the transform defined for corr_constrain(T), which is the inverse hyperbolic tangent,

$f^{-1}(y) = \mbox{atanh}\, y = \frac{1}{2} \log \frac{y + 1}{y - 1}$ .

Parameters

y	Correlation scalar input.

Returns: Free scalar that transforms to the specified input.

Template Parameters

T	Type of scalar.

Definition at line 995 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::corr_matrix_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type	k
	)

Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values.

The input vector must be of length ${k \choose 2} = \frac{k(k-1)}{2}$ . The values in the input vector represent unconstrained (partial) correlations among the dimensions.

The transform based on partial correlations is as specified in

Lewandowski, Daniel, Dorota Kurowicka, and Harry Joe. 2009. Generating random correlation matrices based on vines and extended onion method. Journal of Multivariate Analysis 100:1989–-2001.

The free vector entries are first constrained to be valid correlation values using corr_constrain(T).

Parameters

x	Vector of unconstrained partial correlations.
k	Dimensionality of returned correlation matrix.

Template Parameters

T	Type of scalar.

Exceptions

std::invalid_argument if x is not a valid correlation matrix.

Definition at line 1644 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::corr_matrix_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type	k,
		T &	lp
	)

Return the correlation matrix of the specified dimensionality derived from the specified vector of unconstrained values.

The input vector must be of length ${k \choose 2} = \frac{k(k-1)}{2}$ . The values in the input vector represent unconstrained (partial) correlations among the dimensions.

The transform is as specified for corr_matrix_constrain(Matrix,size_t); the paper it cites also defines the Jacobians for correlation inputs, which are composed with the correlation constrained Jacobians defined in corr_constrain(T,double) for this function.

Parameters

x	Vector of unconstrained partial correlations.
k	Dimensionality of returned correlation matrix.
lp	Log probability reference to increment.

Template Parameters

T	Type of scalar.

Definition at line 1682 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::corr_matrix_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & y )

Return the vector of unconstrained partial correlations that define the specified correlation matrix when transformed.

The constraining transform is defined as for corr_matrix_constrain(Matrix,size_t). The inverse transform in this function is simpler in that it only needs to compute the $k \choose 2$ partial correlations and then free those.

Parameters

y	The correlation matrix to free.

Returns: Vector of unconstrained values that produce the specified correlation matrix when transformed.

Template Parameters

T	Type of scalar.

Exceptions

std::domain_error	if the correlation matrix has no elements or is not a square matrix.
std::runtime_error	if the correlation matrix cannot be factorized by factor_cov_matrix() or if the sds returned by factor_cov_matrix() on log scale are unconstrained.

Definition at line 1722 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cov_matrix_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, 1 > >::type	K
	)

Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2).

See cov_matrix_free() for the inverse transform.

Parameters

x	The vector to convert to a covariance matrix.
K	The number of rows and columns of the resulting covariance matrix.

Exceptions

std::domain_error if (x.size() != K + (K choose 2)).

Definition at line 1769 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cov_matrix_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		typename math::index_type< Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > >::type	K,
		T &	lp
	)

Return the symmetric, positive-definite matrix of dimensions K by K resulting from transforming the specified finite vector of size K plus (K choose 2).

See cov_matrix_free() for the inverse transform.

Parameters

x	The vector to convert to a covariance matrix.
K	The dimensions of the resulting covariance matrix.
lp	Reference

Exceptions

std::domain_error if (x.size() != K + (K choose 2)).

Definition at line 1808 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cov_matrix_constrain_lkj	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		size_t	k
	)

Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values.

The input vector must be of length $k \choose 2 + k$ . The first $k \choose 2$ values in the input represent unconstrained (partial) correlations and the last $k$ are unconstrained standard deviations of the dimensions.

The transform scales the correlation matrix transform defined in corr_matrix_constrain(Matrix,size_t) with the constrained deviations.

Parameters

x	Input vector of unconstrained partial correlations and standard deviations.
k	Dimensionality of returned covariance matrix.

Returns: Covariance matrix derived from the unconstrained partial correlations and deviations.

Template Parameters

T	Type of scalar.

Definition at line 1910 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::cov_matrix_constrain_lkj	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		size_t	k,
		T &	lp
	)

Return the covariance matrix of the specified dimensionality derived from constraining the specified vector of unconstrained values and increment the specified log probability reference with the log absolute Jacobian determinant.

The transform is defined as for cov_matrix_constrain(Matrix,size_t).

The log absolute Jacobian determinant is derived by composing the log absolute Jacobian determinant for the underlying correlation matrix as defined in cov_matrix_constrain(Matrix,size_t,T&) with the Jacobian of the transfrom of the correlation matrix into a covariance matrix by scaling by standard deviations.

Parameters

x	Input vector of unconstrained partial correlations and standard deviations.
k	Dimensionality of returned covariance matrix.
lp	Log probability reference to increment.

Returns: Covariance matrix derived from the unconstrained partial correlations and deviations.

Template Parameters

T	Type of scalar.

Definition at line 1949 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::cov_matrix_free ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & y )

The covariance matrix derived from the symmetric view of the lower-triangular view of the K by K specified matrix is freed to return a vector of size K + (K choose 2).

This is the inverse of the cov_matrix_constrain() function so that for any finite vector x of size K

(K choose 2),

x == cov_matrix_free(cov_matrix_constrain(x,K)).

In order for this round-trip to work (and really for this function to work), the symmetric view of its lower-triangular view must be positive definite.

Parameters

y	Matrix of dimensions K by K such that he symmetric view of the lower-triangular view is positive definite.

Returns: Vector of size K plus (K choose 2) in (-inf,inf) that produces

Exceptions

std::domain_error if y is not square, has zero dimensionality, or has a non-positive diagonal element.

Definition at line 1863 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::cov_matrix_free_lkj ( const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > & y )

Return the vector of unconstrained partial correlations and deviations that transform to the specified covariance matrix.

The constraining transform is defined as for cov_matrix_constrain(Matrix,size_t). The inverse first factors out the deviations, then applies the freeing transfrom of corr_matrix_free(Matrix&).

Parameters

y	Covariance matrix to free.

Returns: Vector of unconstrained values that transforms to the specified covariance matrix.

Template Parameters

T	Type of scalar.

Exceptions

std::domain_error	if the correlation matrix has no elements or is not a square matrix.
std::runtime_error	if the correlation matrix cannot be factorized by factor_cov_matrix()

Definition at line 1983 of file transform.hpp.

template<bool propto, typename T_prob , typename T_prior_sample_size >

boost::math::tools::promote_args<T_prob,T_prior_sample_size>::type stan::prob::dirichlet_log	(	const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta,
		const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &	alpha
	)

The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha.

Each element of alpha must be greater than 0. Each element of theta must be greater than or 0. Theta sums to 1.

$\begin{eqnarray*} \theta &\sim& \mbox{\sf{Dirichlet}} (\alpha_1, \ldots, \alpha_k) \\ \log (p (\theta \,|\, \alpha_1, \ldots, \alpha_k) ) &=& \log \left( \frac{\Gamma(\alpha_1 + \cdots + \alpha_k)}{\Gamma(\alpha_1) \cdots \Gamma(\alpha_k)} \theta_1^{\alpha_1 - 1} \cdots \theta_k^{\alpha_k - 1} \right) \\ &=& \log (\Gamma(\alpha_1 + \cdots + \alpha_k)) - \log(\Gamma(\alpha_1)) - \cdots - \log(\Gamma(\alpha_k)) + (\alpha_1 - 1) \log (\theta_1) + \cdots + (\alpha_k - 1) \log (\theta_k) \end{eqnarray*}$

Parameters

theta	A scalar vector.
alpha	Prior sample sizes.

Returns: The log of the Dirichlet density.

Exceptions

std::domain_error	if any element of alpha is less than or equal to 0.
std::domain_error	if any element of theta is less than 0.
std::domain_error	if the sum of theta is not 1.

Template Parameters

T_prob	Type of scalar.
T_prior_sample_size	Type of prior sample sizes.

Definition at line 46 of file dirichlet.hpp.

template<typename T_prob , typename T_prior_sample_size >

boost::math::tools::promote_args<T_prob,T_prior_sample_size>::type stan::prob::dirichlet_log	(	const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta,
		const Eigen::Matrix< T_prior_sample_size, Eigen::Dynamic, 1 > &	alpha
	)

inline

Definition at line 77 of file dirichlet.hpp.

template<class RNG >

Eigen::VectorXd stan::prob::dirichlet_rng	(	const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	alpha,
		RNG &	rng
	)

inline

Definition at line 84 of file dirichlet.hpp.

template<typename T_shape >

T_shape stan::prob::do_lkj_constant	(	const T_shape &	eta,
		const unsigned int &	K
	)

Definition at line 15 of file lkj_corr.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::double_exponential_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 291 of file double_exponential.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::double_exponential_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Calculates the double exponential cumulative density function.

$f(y|\mu,\sigma) = \begin{cases} \ \frac{1}{2} \exp\left(\frac{y-\mu}{\sigma}\right), \mbox{if } y < \mu \\ 1 - \frac{1}{2} \exp\left(-\frac{y-\mu}{\sigma}\right), \mbox{if } y \ge \mu \ \end{cases}$

Parameters

y	A scalar variate.
mu	The location parameter.
sigma	The scale parameter.

Returns: The cumulative density function.

Definition at line 138 of file double_exponential.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::double_exponential_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 215 of file double_exponential.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::double_exponential_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 24 of file double_exponential.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::double_exponential_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 117 of file double_exponential.hpp.

template<class RNG >

double stan::prob::double_exponential_rng	(	const double	mu,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 367 of file double_exponential.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >

return_type<T_y,T_loc,T_scale,T_inv_scale>::type stan::prob::exp_mod_normal_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_inv_scale &	lambda
	)

Definition at line 356 of file exp_mod_normal.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >

return_type<T_y,T_loc,T_scale,T_inv_scale>::type stan::prob::exp_mod_normal_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_inv_scale &	lambda
	)

Definition at line 140 of file exp_mod_normal.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >

return_type<T_y,T_loc,T_scale,T_inv_scale>::type stan::prob::exp_mod_normal_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_inv_scale &	lambda
	)

Definition at line 252 of file exp_mod_normal.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >

return_type<T_y,T_loc,T_scale, T_inv_scale>::type stan::prob::exp_mod_normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_inv_scale &	lambda
	)

Definition at line 26 of file exp_mod_normal.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >

return_type<T_y,T_loc,T_scale, T_inv_scale>::type stan::prob::exp_mod_normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_inv_scale &	lambda
	)

inline

Definition at line 132 of file exp_mod_normal.hpp.

template<class RNG >

double stan::prob::exp_mod_normal_rng	(	const double	mu,
		const double	sigma,
		const double	lambda,
		RNG &	rng
	)

inline

Definition at line 458 of file exp_mod_normal.hpp.

template<typename T_y , typename T_inv_scale >

return_type<T_y,T_inv_scale>::type stan::prob::exponential_ccdf_log	(	const T_y &	y,
		const T_inv_scale &	beta
	)

Definition at line 221 of file exponential.hpp.

template<typename T_y , typename T_inv_scale >

return_type<T_y,T_inv_scale>::type stan::prob::exponential_cdf	(	const T_y &	y,
		const T_inv_scale &	beta
	)

Calculates the exponential cumulative distribution function for the given y and beta.

Inverse scale parameter must be greater than 0. y must be greater than or equal to 0.

Parameters

y	A scalar variable.
beta	Inverse scale parameter.

Template Parameters

T_y	Type of scalar.
T_inv_scale	Type of inverse scale.
Policy	Error-handling policy.

Definition at line 122 of file exponential.hpp.

template<typename T_y , typename T_inv_scale >

return_type<T_y,T_inv_scale>::type stan::prob::exponential_cdf_log	(	const T_y &	y,
		const T_inv_scale &	beta
	)

Definition at line 175 of file exponential.hpp.

template<bool propto, typename T_y , typename T_inv_scale >

return_type<T_y,T_inv_scale>::type stan::prob::exponential_log	(	const T_y &	y,
		const T_inv_scale &	beta
	)

The log of an exponential density for y with the specified inverse scale parameter.

Inverse scale parameter must be greater than 0. y must be greater than or equal to 0.

$\begin{eqnarray*} y &\sim& \mbox{\sf{Expon}}(\beta) \\ \log (p (y \,|\, \beta) ) &=& \log \left( \beta \exp^{-\beta y} \right) \\ &=& \log (\beta) - \beta y \\ & & \mathrm{where} \; y > 0 \end{eqnarray*}$

Parameters

y	A scalar variable.
beta	Inverse scale parameter.

Exceptions

std::domain_error	if beta is not greater than 0.
std::domain_error	if y is not greater than or equal to 0.

Template Parameters

T_y	Type of scalar.
T_inv_scale	Type of inverse scale.

Definition at line 46 of file exponential.hpp.

template<typename T_y , typename T_inv_scale >

return_type<T_y,T_inv_scale>::type stan::prob::exponential_log	(	const T_y &	y,
		const T_inv_scale &	beta
	)

inline

Definition at line 101 of file exponential.hpp.

template<class RNG >

double stan::prob::exponential_rng	(	const double	beta,
		RNG &	rng
	)

inline

Definition at line 265 of file exponential.hpp.

template<typename T >

bool stan::prob::factor_cov_matrix	(	const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		Eigen::Array< T, Eigen::Dynamic, 1 > &	sds
	)

This function is intended to make starting values, given a covariance matrix Sigma.

The transformations are hard coded as log for standard deviations and Fisher transformations (atanh()) of CPCs

Parameters

[in]	Sigma	covariance matrix
[out]	CPCs	fill this unbounded (does not resize)
[out]	sds	fill this unbounded (does not resize)

Returns: false if any of the diagonals of Sigma are 0

Definition at line 88 of file transform.hpp.

template<typename T >

void stan::prob::factor_U	(	const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &	U,
		Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs
	)

This function is intended to make starting values, given a unit upper-triangular matrix U such that U'DU is a correlation matrix.

Parameters

CPCs	fill this unbounded
Sigma	U matrix

Definition at line 43 of file transform.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::frechet_ccdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 244 of file frechet.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::frechet_cdf	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 131 of file frechet.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::frechet_cdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 193 of file frechet.hpp.

template<bool propto, typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::frechet_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 24 of file frechet.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::frechet_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

inline

Definition at line 125 of file frechet.hpp.

template<class RNG >

double stan::prob::frechet_rng	(	const double	alpha,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 297 of file frechet.hpp.

template<typename T_y , typename T_shape , typename T_inv_scale >

return_type<T_y,T_shape,T_inv_scale>::type stan::prob::gamma_ccdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

Definition at line 388 of file gamma.hpp.

template<typename T_y , typename T_shape , typename T_inv_scale >

return_type<T_y,T_shape,T_inv_scale>::type stan::prob::gamma_cdf	(	const T_y &	y,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

The cumulative density function for a gamma distribution for y with the specified shape and inverse scale parameters.

Parameters

y	A scalar variable.
alpha	Shape parameter.
beta	Inverse scale parameter.

Exceptions

std::domain_error	if alpha is not greater than 0.
std::domain_error	if beta is not greater than 0.
std::domain_error	if y is not greater than or equal to 0.

Template Parameters

T_y	Type of scalar.
T_shape	Type of shape.
T_inv_scale	Type of inverse scale.

Definition at line 172 of file gamma.hpp.

template<typename T_y , typename T_shape , typename T_inv_scale >

return_type<T_y,T_shape,T_inv_scale>::type stan::prob::gamma_cdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

Definition at line 285 of file gamma.hpp.

template<bool propto, typename T_y , typename T_shape , typename T_inv_scale >

return_type<T_y,T_shape,T_inv_scale>::type stan::prob::gamma_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

The log of a gamma density for y with the specified shape and inverse scale parameters.

Shape and inverse scale parameters must be greater than 0. y must be greater than or equal to 0.

$\begin{eqnarray*} y &\sim& \mbox{\sf{Gamma}}(\alpha, \beta) \\ \log (p (y \,|\, \alpha, \beta) ) &=& \log \left( \frac{\beta^\alpha}{\Gamma(\alpha)} y^{\alpha - 1} \exp^{- \beta y} \right) \\ &=& \alpha \log(\beta) - \log(\Gamma(\alpha)) + (\alpha - 1) \log(y) - \beta y\\ & & \mathrm{where} \; y > 0 \end{eqnarray*}$

Parameters

y	A scalar variable.
alpha	Shape parameter.
beta	Inverse scale parameter.

Exceptions

std::domain_error	if alpha is not greater than 0.
std::domain_error	if beta is not greater than 0.
std::domain_error	if y is not greater than or equal to 0.

Template Parameters

T_y	Type of scalar.
T_shape	Type of shape.
T_inv_scale	Type of inverse scale.

Definition at line 46 of file gamma.hpp.

template<typename T_y , typename T_shape , typename T_inv_scale >

return_type<T_y,T_shape,T_inv_scale>::type stan::prob::gamma_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

inline

Definition at line 151 of file gamma.hpp.

template<class RNG >

double stan::prob::gamma_rng	(	const double	alpha,
		const double	beta,
		RNG &	rng
	)

inline

Definition at line 491 of file gamma.hpp.

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >

return_type< T_y, typename return_type<T_F,T_G,T_V,T_W,T_m0,T_C0>::type >::type stan::prob::gaussian_dlm_obs_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &	F,
		const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &	G,
		const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &	V,
		const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &	m0,
		const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &	C0
	)

The log of a Gaussian dynamic linear model (GDLM).

This distribution is equivalent to, for $t = 1:T$ ,

$\begin{eqnarray*} y_t & \sim N(F' \theta_t, V) \\ \theta_t & \sim N(G \theta_{t-1}, W) \\ \theta_0 & \sim N(m_0, C_0) \end{eqnarray*}$

If V is a vector, then the Kalman filter is applied sequentially.

Parameters

y	A r x T matrix of observations. Rows are variables, columns are observations.
F	A n x r matrix. The design matrix.
G	A n x n matrix. The transition matrix.
V	A r x r matrix. The observation covariance matrix.
W	A n x n matrix. The state covariance matrix.
m0	A n x 1 matrix. The mean vector of the distribution of the initial state.
C0	A n x n matrix. The covariance matrix of the distribution of the initial state.

Returns: The log of the joint density of the GDLM.

Exceptions

std::domain_error if a matrix in the Kalman filter is not positive semi-definite.

Template Parameters

T_y	Type of scalar.
T_F	Type of design matrix.
T_G	Type of transition matrix.
T_V	Type of observation covariance matrix.
T_W	Type of state covariance matrix.
T_m0	Type of initial state mean vector.
T_C0	Type of initial state covariance matrix.

Definition at line 80 of file gaussian_dlm_obs.hpp.

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >

return_type< T_y, typename return_type<T_F,T_G,T_V,T_W,T_m0,T_C0>::type >::type stan::prob::gaussian_dlm_obs_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &	F,
		const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &	G,
		const Eigen::Matrix< T_V, Eigen::Dynamic, Eigen::Dynamic > &	V,
		const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &	m0,
		const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &	C0
	)

inline

Definition at line 234 of file gaussian_dlm_obs.hpp.

template<bool propto, typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >

return_type< T_y, typename return_type<T_F,T_G,T_V,T_W,T_m0,T_C0>::type >::type stan::prob::gaussian_dlm_obs_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &	F,
		const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &	G,
		const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &	V,
		const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &	m0,
		const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &	C0
	)

The log of a Gaussian dynamic linear model (GDLM) with uncorrelated observation disturbances.

This distribution is equivalent to, for $t = 1:T$ ,

$\begin{eqnarray*} y_t & \sim N(F' \theta_t, diag(V)) \\ \theta_t & \sim N(G \theta_{t-1}, W) \\ \theta_0 & \sim N(m_0, C_0) \end{eqnarray*}$

If V is a vector, then the Kalman filter is applied sequentially.

Parameters

y	A r x T matrix of observations. Rows are variables, columns are observations.
F	A n x r matrix. The design matrix.
G	A n x n matrix. The transition matrix.
V	A size r vector. The diagonal of the observation covariance matrix.
W	A n x n matrix. The state covariance matrix.
m0	A n x 1 matrix. The mean vector of the distribution of the initial state.
C0	A n x n matrix. The covariance matrix of the distribution of the initial state.

Returns: The log of the joint density of the GDLM.

Exceptions

std::domain_error if a matrix in the Kalman filter is not semi-positive definite.

Template Parameters

T_y	Type of scalar.
T_F	Type of design matrix.
T_G	Type of transition matrix.
T_V	Type of observation variances
T_W	Type of state covariance matrix.
T_m0	Type of initial state mean vector.
T_C0	Type of initial state covariance matrix.

Definition at line 288 of file gaussian_dlm_obs.hpp.

template<typename T_y , typename T_F , typename T_G , typename T_V , typename T_W , typename T_m0 , typename T_C0 >

return_type< T_y, typename return_type<T_F,T_G,T_V,T_W,T_m0,T_C0>::type >::type stan::prob::gaussian_dlm_obs_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_F, Eigen::Dynamic, Eigen::Dynamic > &	F,
		const Eigen::Matrix< T_G, Eigen::Dynamic, Eigen::Dynamic > &	G,
		const Eigen::Matrix< T_V, Eigen::Dynamic, 1 > &	V,
		const Eigen::Matrix< T_W, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const Eigen::Matrix< T_m0, Eigen::Dynamic, 1 > &	m0,
		const Eigen::Matrix< T_C0, Eigen::Dynamic, Eigen::Dynamic > &	C0
	)

inline

Definition at line 447 of file gaussian_dlm_obs.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::gumbel_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	beta
	)

Definition at line 234 of file gumbel.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::gumbel_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	beta
	)

Definition at line 113 of file gumbel.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::gumbel_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	beta
	)

Definition at line 181 of file gumbel.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::gumbel_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	beta
	)

Definition at line 21 of file gumbel.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::gumbel_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	beta
	)

inline

Definition at line 107 of file gumbel.hpp.

template<class RNG >

double stan::prob::gumbel_rng	(	const double	mu,
		const double	beta,
		RNG &	rng
	)

inline

Definition at line 289 of file gumbel.hpp.

template<bool propto, typename T_n , typename T_N , typename T_a , typename T_b >

double stan::prob::hypergeometric_log	(	const T_n &	n,
		const T_N &	N,
		const T_a &	a,
		const T_b &	b
	)

Definition at line 25 of file hypergeometric.hpp.

template<typename T_n , typename T_N , typename T_a , typename T_b >

double stan::prob::hypergeometric_log	(	const T_n &	n,
		const T_N &	N,
		const T_a &	a,
		const T_b &	b
	)

inline

Definition at line 83 of file hypergeometric.hpp.

template<class RNG >

int stan::prob::hypergeometric_rng	(	const int	N,
		const int	a,
		const int	b,
		RNG &	rng
	)

inline

Definition at line 92 of file hypergeometric.hpp.

template<typename T >

T stan::prob::identity_constrain ( T x )

inline

Returns the result of applying the identity constraint transform to the input.

This method is effectively a no-op and is mainly useful as a placeholder in auto-generated code.

Parameters

x	Free scalar.

Returns: Transformed input.

Template Parameters

T	Type of scalar.

Definition at line 391 of file transform.hpp.

template<typename T >

T stan::prob::identity_constrain	(	const T	x,
		T &
	)

inline

Returns the result of applying the identity constraint transform to the input and increments the log probability reference with the log absolute Jacobian determinant.

This method is effectively a no-op and mainly useful as a placeholder in auto-generated code.

Parameters

x	Free scalar. lp Reference to log probability.

Returns: Transformed input.

Template Parameters

T	Type of scalar.

Definition at line 410 of file transform.hpp.

template<typename T >

T stan::prob::identity_free ( const T y )

inline

Returns the result of applying the inverse of the identity constraint transform to the input.

This method is effectively a no-op and mainly useful as a placeholder in auto-generated code.

Parameters

y	Constrained scalar.

Returns: The input.

Template Parameters

T	Type of scalar.

Definition at line 427 of file transform.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::inv_chi_square_ccdf_log	(	const T_y &	y,
		const T_dof &	nu
	)

Definition at line 332 of file inv_chi_square.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::inv_chi_square_cdf	(	const T_y &	y,
		const T_dof &	nu
	)

Definition at line 137 of file inv_chi_square.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::inv_chi_square_cdf_log	(	const T_y &	y,
		const T_dof &	nu
	)

Definition at line 239 of file inv_chi_square.hpp.

template<bool propto, typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::inv_chi_square_log	(	const T_y &	y,
		const T_dof &	nu
	)

The log of an inverse chi-squared density for y with the specified degrees of freedom parameter.

The degrees of freedom prarameter must be greater than 0. y must be greater than 0.

$\begin{eqnarray*} y &\sim& \mbox{\sf{Inv-}}\chi^2_\nu \\ \log (p (y \,|\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)} y^{- (\nu / 2 + 1)} \exp^{-1 / (2y)} \right) \\ &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) - (\frac{\nu}{2} + 1) \log(y) - \frac{1}{2y} \\ & & \mathrm{ where } \; y > 0 \end{eqnarray*}$

Parameters

y	A scalar variable.
nu	Degrees of freedom.

Exceptions

std::domain_error	if nu is not greater than or equal to 0
std::domain_error	if y is not greater than or equal to 0.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.

Definition at line 43 of file inv_chi_square.hpp.

template<typename T_y , typename T_dof >

return_type<T_y,T_dof>::type stan::prob::inv_chi_square_log	(	const T_y &	y,
		const T_dof &	nu
	)

inline

Definition at line 131 of file inv_chi_square.hpp.

template<class RNG >

double stan::prob::inv_chi_square_rng	(	const double	nu,
		RNG &	rng
	)

inline

Definition at line 425 of file inv_chi_square.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::inv_gamma_ccdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	beta
	)

Definition at line 401 of file inv_gamma.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::inv_gamma_cdf	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	beta
	)

The CDF of an inverse gamma density for y with the specified shape and scale parameters.

y, shape, and scale parameters must be greater than 0.

Parameters

y	A scalar variable.
alpha	Shape parameter.
beta	Scale parameter.

Exceptions

std::domain_error	if alpha is not greater than 0.
std::domain_error	if beta is not greater than 0.
std::domain_error	if y is not greater than 0.

Template Parameters

T_y	Type of scalar.
T_shape	Type of shape.
T_scale	Type of scale.

Definition at line 177 of file inv_gamma.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::inv_gamma_cdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	beta
	)

Definition at line 294 of file inv_gamma.hpp.

template<bool propto, typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::inv_gamma_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	beta
	)

The log of an inverse gamma density for y with the specified shape and scale parameters.

Shape and scale parameters must be greater than 0. y must be greater than 0.

Parameters

y	A scalar variable.
alpha	Shape parameter.
beta	Scale parameter.

Exceptions

std::domain_error	if alpha is not greater than 0.
std::domain_error	if beta is not greater than 0.
std::domain_error	if y is not greater than 0.

Template Parameters

T_y	Type of scalar.
T_shape	Type of shape.
T_scale	Type of scale.

Definition at line 40 of file inv_gamma.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::inv_gamma_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	beta
	)

inline

Definition at line 155 of file inv_gamma.hpp.

template<class RNG >

double stan::prob::inv_gamma_rng	(	const double	alpha,
		const double	beta,
		RNG &	rng
	)

inline

Definition at line 508 of file inv_gamma.hpp.

template<bool propto, typename T_y , typename T_dof , typename T_scale >

boost::math::tools::promote_args<T_y,T_dof,T_scale>::type stan::prob::inv_wishart_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const T_dof &	nu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &	S
	)

The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix.

The scale matrix, S, must be k x k, symmetric, and semi-positive definite.

$\begin{eqnarray*} W &\sim& \mbox{\sf{Inv-Wishart}}_{\nu} (S) \\ \log (p (W \,|\, \nu, S) ) &=& \log \left( \left(2^{\nu k/2} \pi^{k (k-1) /4} \prod_{i=1}^k{\Gamma (\frac{\nu + 1 - i}{2})} \right)^{-1} \times \left| S \right|^{\nu/2} \left| W \right|^{-(\nu + k + 1) / 2} \times \exp (-\frac{1}{2} \mbox{tr} (S W^{-1})) \right) \\ &=& -\frac{\nu k}{2}\log(2) - \frac{k (k-1)}{4} \log(\pi) - \sum_{i=1}^{k}{\log (\Gamma (\frac{\nu+1-i}{2}))} +\frac{\nu}{2} \log(\det(S)) - \frac{\nu+k+1}{2}\log (\det(W)) - \frac{1}{2} \mbox{tr}(S W^{-1}) \end{eqnarray*}$

Parameters

W	A scalar matrix
nu	Degrees of freedom
S	The scale matrix

Returns: The log of the Inverse-Wishart density at W given nu and S.

Exceptions

std::domain_error	if nu is not greater than k-1
std::domain_error	if S is not square, not symmetric, or not semi-positive definite.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.
T_scale	Type of scale.

Definition at line 52 of file inv_wishart.hpp.

template<typename T_y , typename T_dof , typename T_scale >

boost::math::tools::promote_args<T_y,T_dof,T_scale>::type stan::prob::inv_wishart_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const T_dof &	nu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &	S
	)

inline

Definition at line 125 of file inv_wishart.hpp.

template<class RNG >

Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> stan::prob::inv_wishart_rng	(	const double	nu,
		const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &	S,
		RNG &	rng
	)

inline

Definition at line 133 of file inv_wishart.hpp.

template<typename T , typename TL >

T stan::prob::lb_constrain	(	const T	x,
		const TL	lb
	)

inline

Return the lower-bounded value for the specified unconstrained input and specified lower bound.

The transform applied is

$f(x) = \exp(x) + L$

where $L$ is the constant lower bound.

If the lower bound is negative infinity, this function reduces to identity_constrain(x).

Parameters

x	Unconstrained scalar input.
lb	Lower-bound on constrained ouptut.

Returns: Lower-bound constrained value correspdonding to inputs.

Template Parameters

T	Type of scalar.
TL	Type of lower bound.

Definition at line 520 of file transform.hpp.

template<typename T , typename TL >

boost::math::tools::promote_args<T,TL>::type stan::prob::lb_constrain	(	const T	x,
		const TL	lb,
		T &	lp
	)

inline

Return the lower-bounded value for the speicifed unconstrained input and specified lower bound, incrementing the specified reference with the log absolute Jacobian determinant of the transform.

If the lower bound is negative infinity, this function reduces to identity_constraint(x,lp).

Parameters

x	Unconstrained scalar input.
lb	Lower-bound on output.
lp	Reference to log probability to increment.

Returns: Loer-bound constrained value corresponding to inputs.

Template Parameters

T	Type of scalar.
TL	Type of lower bound.

Definition at line 545 of file transform.hpp.

template<typename T , typename TL >

boost::math::tools::promote_args<T,TL>::type stan::prob::lb_free	(	const T	y,
		const TL	lb
	)

inline

Return the unconstrained value that produces the specified lower-bound constrained value.

If the lower bound is negative infinity, it is ignored and the function reduces to identity_free(y).

Parameters

y	Input scalar.
lb	Lower bound.

Returns: Unconstrained value that produces the input when constrained.

Template Parameters

T	Type of scalar.
TL	Type of lower bound.

Exceptions

std::domain_error if y is lower than the lower bound.

Definition at line 570 of file transform.hpp.

template<bool propto, typename T_covar , typename T_shape >

boost::math::tools::promote_args<T_covar, T_shape>::type stan::prob::lkj_corr_cholesky_log	(	const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	L,
		const T_shape &	eta
	)

Definition at line 48 of file lkj_corr.hpp.

template<typename T_covar , typename T_shape >

boost::math::tools::promote_args<T_covar, T_shape>::type stan::prob::lkj_corr_cholesky_log	(	const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	L,
		const T_shape &	eta
	)

inline

Definition at line 92 of file lkj_corr.hpp.

template<class RNG >

Eigen::MatrixXd stan::prob::lkj_corr_cholesky_rng	(	const size_t	K,
		const double	eta,
		RNG &	rng
	)

inline

Definition at line 153 of file lkj_corr.hpp.

template<bool propto, typename T_y , typename T_shape >

boost::math::tools::promote_args<T_y, T_shape>::type stan::prob::lkj_corr_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const T_shape &	eta
	)

Definition at line 103 of file lkj_corr.hpp.

template<typename T_y , typename T_shape >

boost::math::tools::promote_args<T_y, T_shape>::type stan::prob::lkj_corr_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const T_shape &	eta
	)

inline

Definition at line 146 of file lkj_corr.hpp.

template<class RNG >

Eigen::MatrixXd stan::prob::lkj_corr_rng	(	const size_t	K,
		const double	eta,
		RNG &	rng
	)

inline

Definition at line 178 of file lkj_corr.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >

boost::math::tools::promote_args<T_y,T_loc,T_scale,T_shape>::type stan::prob::lkj_cov_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &	mu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &	sigma,
		const T_shape &	eta
	)

Definition at line 23 of file lkj_cov.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

boost::math::tools::promote_args<T_y,T_loc,T_scale,T_shape>::type stan::prob::lkj_cov_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_loc, Eigen::Dynamic, 1 > &	mu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, 1 > &	sigma,
		const T_shape &	eta
	)

inline

Definition at line 76 of file lkj_cov.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >

boost::math::tools::promote_args<T_y,T_loc,T_scale,T_shape>::type stan::prob::lkj_cov_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_shape &	eta
	)

Definition at line 88 of file lkj_cov.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

boost::math::tools::promote_args<T_y,T_loc,T_scale,T_shape>::type stan::prob::lkj_cov_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_shape &	eta
	)

inline

Definition at line 124 of file lkj_cov.hpp.

template<typename T >

T stan::prob::log_inv_logit_diff	(	const T &	alpha,
		const T &	beta
	)

inline

Definition at line 24 of file ordered_logistic.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y, T_loc, T_scale>::type stan::prob::logistic_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 315 of file logistic.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y, T_loc, T_scale>::type stan::prob::logistic_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 143 of file logistic.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y, T_loc, T_scale>::type stan::prob::logistic_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 237 of file logistic.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::logistic_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 27 of file logistic.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::logistic_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

inline

Definition at line 136 of file logistic.hpp.

template<class RNG >

double stan::prob::logistic_rng	(	const double	mu,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 393 of file logistic.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::lognormal_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 292 of file lognormal.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::lognormal_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 150 of file lognormal.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::lognormal_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 225 of file lognormal.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::lognormal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 24 of file lognormal.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::lognormal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

inline

Definition at line 143 of file lognormal.hpp.

template<class RNG >

double stan::prob::lognormal_rng	(	const double	mu,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 360 of file lognormal.hpp.

template<typename T , typename TL , typename TU >

boost::math::tools::promote_args<T,TL,TU>::type stan::prob::lub_constrain	(	const T	x,
		TL	lb,
		TU	ub
	)

inline

Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds.

The transform is the transformed and scaled inverse logit,

$f(x) = L + (U - L) \mbox{logit}^{-1}(x)$

If the lower bound is negative infinity and upper bound finite, this function reduces to ub_constrain(x,ub). If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_constrain(x,lb). If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_constrain(x).

Parameters

x	Free scalar to transform.
lb	Lower bound.
ub	Upper bound.

Returns: Lower- and upper-bounded scalar derived from transforming the free scalar.

Template Parameters

T	Type of scalar.
TL	Type of lower bound.
TU	Type of upper bound.

Exceptions

std::domain_error if ub <= lb

Definition at line 710 of file transform.hpp.

template<typename T , typename TL , typename TU >

boost::math::tools::promote_args<T,TL,TU>::type stan::prob::lub_constrain	(	const T	x,
		const TL	lb,
		const TU	ub,
		T &	lp
	)

Return the lower- and upper-bounded scalar derived by transforming the specified free scalar given the specified lower and upper bounds and increment the specified log probability with the log absolute Jacobian determinant.

The transform is as defined in lub_constrain(T,double,double). The log absolute Jacobian determinant is given by

$\log \left| \frac{d}{dx} \left( L + (U-L) \mbox{logit}^{-1}(x) \right) \right|$

${} = \log | (U-L) \, (\mbox{logit}^{-1}(x)) \, (1 - \mbox{logit}^{-1}(x)) |$

${} = \log (U - L) + \log (\mbox{logit}^{-1}(x)) + \log (1 - \mbox{logit}^{-1}(x))$

If the lower bound is negative infinity and upper bound finite, this function reduces to ub_constrain(x,ub,lp). If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_constrain(x,lb,lp). If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_constrain(x,lp).

Parameters

x	Free scalar to transform.
lb	Lower bound.
ub	Upper bound.
lp	Log probability scalar reference.

Returns: Lower- and upper-bounded scalar derived from transforming the free scalar.

Template Parameters

T	Type of scalar.
TL	Type of lower bound.
TU	Type of upper bound.

Exceptions

std::domain_error if ub <= lb

Definition at line 780 of file transform.hpp.

template<typename T , typename TL , typename TU >

boost::math::tools::promote_args<T,TL,TU>::type stan::prob::lub_free	(	const T	y,
		TL	lb,
		TU	ub
	)

inline

Return the unconstrained scalar that transforms to the specified lower- and upper-bounded scalar given the specified bounds.

The transfrom in lub_constrain(T,double,double), is reversed by a transformed and scaled logit,

$f^{-1}(y) = \mbox{logit}(\frac{y - L}{U - L})$

where $U$ and $L$ are the lower and upper bounds.

If the lower bound is negative infinity and upper bound finite, this function reduces to ub_free(y,ub). If the upper bound is positive infinity and the lower bound finite, this function reduces to lb_free(x,lb). If the upper bound is positive infinity and the lower bound negative infinity, this function reduces to identity_free(y).

Template Parameters

T	Type of scalar.

Parameters

y	Scalar input.
lb	Lower bound.
ub	Upper bound.

Returns: The free scalar that transforms to the input scalar given the bounds.

Exceptions

std::invalid_argument if the lower bound is greater than the upper bound, y is less than the lower bound, or y is greater than the upper bound

Definition at line 845 of file transform.hpp.

template<typename T >

const Eigen::Array<T,Eigen::Dynamic,1> stan::prob::make_nu	(	const T	eta,
		const size_t	K
	)

This function calculates the degrees of freedom for the t distribution that corresponds to the shape parameter in the Lewandowski et.

al. distribution

Parameters

eta	hyperparameter on (0,inf), eta = 1 <-> correlation matrix is uniform
K	number of variables in covariance matrix

Definition at line 343 of file transform.hpp.

template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D >

boost::math::tools::promote_args<T_y,T_Mu,T_Sigma,T_D>::type stan::prob::matrix_normal_prec_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &	Mu,
		const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &	D
	)

The log of the matrix normal density for the given y, mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices.

Parameters

y	An mxn matrix.
Mu	The mean matrix.
Sigma	The mxm inverse covariance matrix (i.e., the precision matrix) of the rows of y.
D	The nxn inverse covariance matrix (i.e., the precision matrix) of the columns of y.

Returns: The log of the matrix normal density.

Exceptions

std::domain_error if Sigma or D are not square, not symmetric, or not semi-positive definite.

Template Parameters

T_y	Type of scalar.
T_Mu	Type of location.
T_Sigma	Type of Sigma.
T_D	Type of D.

Definition at line 41 of file matrix_normal.hpp.

template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D >

boost::math::tools::promote_args<T_y,T_Mu,T_Sigma,T_D>::type stan::prob::matrix_normal_prec_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_Mu, Eigen::Dynamic, Eigen::Dynamic > &	Mu,
		const Eigen::Matrix< T_Sigma, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		const Eigen::Matrix< T_D, Eigen::Dynamic, Eigen::Dynamic > &	D
	)

Definition at line 117 of file matrix_normal.hpp.

template<bool propto, typename T_y , typename T_covar , typename T_w >

boost::math::tools::promote_args<T_y,T_covar,T_w>::type stan::prob::multi_gp_cholesky_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	L,
		const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &	w
	)

The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma.

Sigma = LL', a square, semi-positive definite matrix.. y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y,i) ~ multi_normal(0,(1/w[i])*LL').

Parameters

y	A dxN matrix
L	The Cholesky decomposition of a kernel matrix
w	A d-dimensional vector of positve inverse scale parameters for each output.

Returns: The log of the multivariate GP density.

Exceptions

std::domain_error if Sigma is not square, not symmetric, or not semi-positive definite.

Template Parameters

T_y	Type of scalar.
T_covar	Type of kernel.
T_w	Type of weight.

Definition at line 45 of file multi_gp_cholesky.hpp.

template<typename T_y , typename T_covar , typename T_w >

boost::math::tools::promote_args<T_y,T_covar,T_w>::type stan::prob::multi_gp_cholesky_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	L,
		const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &	w
	)

inline

Definition at line 106 of file multi_gp_cholesky.hpp.

template<bool propto, typename T_y , typename T_covar , typename T_w >

boost::math::tools::promote_args<T_y,T_covar,T_w>::type stan::prob::multi_gp_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &	w
	)

The log of a multivariate Gaussian Process for the given y, Sigma, and w.

y is a dxN matrix, where each column is a different observation and each row is a different output dimension. The Gaussian Process is assumed to have a scaled kernel matrix with a different scale for each output dimension. This distribution is equivalent to: for (i in 1:d) row(y,i) ~ multi_normal(0,(1/w[i])*Sigma).

Parameters

y	A dxN matrix
Sigma	The NxN kernel matrix
w	A d-dimensional vector of positve inverse scale parameters for each output.

Returns: The log of the multivariate GP density.

Exceptions

std::domain_error if Sigma is not square, not symmetric, or not semi-positive definite.

Template Parameters

T_y	Type of scalar.
T_covar	Type of kernel.
T_w	Type of weight.

Definition at line 45 of file multi_gp.hpp.

template<typename T_y , typename T_covar , typename T_w >

boost::math::tools::promote_args<T_y,T_covar,T_w>::type stan::prob::multi_gp_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	y,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma,
		const Eigen::Matrix< T_w, Eigen::Dynamic, 1 > &	w
	)

inline

Definition at line 115 of file multi_gp.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_covar >

boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type stan::prob::multi_normal_cholesky_log	(	const T_y &	y,
		const T_loc &	mu,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	L
	)

The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix.

Sigma = LL', a square, semi-positive definite matrix.

Parameters

y	A scalar vector
mu	The mean vector of the multivariate normal distribution.
L	The Cholesky decomposition of a variance matrix of the multivariate normal distribution

Returns: The log of the multivariate normal density.

Exceptions

std::domain_error if LL' is not square, not symmetric, or not semi-positive definite.

Template Parameters

T_y	Type of scalar.
T_loc	Type of location.
T_covar	Type of scale.

Definition at line 53 of file multi_normal_cholesky.hpp.

template<typename T_y , typename T_loc , typename T_covar >

boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type stan::prob::multi_normal_cholesky_log	(	const T_y &	y,
		const T_loc &	mu,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	L
	)

inline

Definition at line 159 of file multi_normal_cholesky.hpp.

template<class RNG >

Eigen::VectorXd stan::prob::multi_normal_cholesky_rng	(	const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	mu,
		const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &	S,
		RNG &	rng
	)

inline

Definition at line 167 of file multi_normal_cholesky.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_covar >

boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type stan::prob::multi_normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma
	)

Definition at line 27 of file multi_normal.hpp.

template<typename T_y , typename T_loc , typename T_covar >

boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type stan::prob::multi_normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma
	)

inline

Definition at line 131 of file multi_normal.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_covar >

boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type stan::prob::multi_normal_prec_log	(	const T_y &	y,
		const T_loc &	mu,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma
	)

Definition at line 34 of file multi_normal_prec.hpp.

template<typename T_y , typename T_loc , typename T_covar >

boost::math::tools::promote_args<typename scalar_type<T_y>::type, typename scalar_type<T_loc>::type, T_covar>::type stan::prob::multi_normal_prec_log	(	const T_y &	y,
		const T_loc &	mu,
		const Eigen::Matrix< T_covar, Eigen::Dynamic, Eigen::Dynamic > &	Sigma
	)

inline

Definition at line 147 of file multi_normal_prec.hpp.

template<class RNG >

Eigen::VectorXd stan::prob::multi_normal_rng	(	const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	mu,
		const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &	S,
		RNG &	rng
	)

inline

Definition at line 139 of file multi_normal.hpp.

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >

boost::math::tools::promote_args<typename scalar_type<T_y>::type,T_dof,typename scalar_type<T_loc>::type,T_scale>::type stan::prob::multi_student_t_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_loc &	mu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &	Sigma
	)

Return the log of the multivariate Student t distribution at the specified arguments.

Template Parameters

propto Carry out calculations up to a proportion

Definition at line 35 of file multi_student_t.hpp.

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >

boost::math::tools::promote_args<typename scalar_type<T_y>::type,T_dof,typename scalar_type<T_loc>::type,T_scale>::type stan::prob::multi_student_t_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_loc &	mu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &	Sigma
	)

inline

Definition at line 172 of file multi_student_t.hpp.

template<class RNG >

Eigen::VectorXd stan::prob::multi_student_t_rng	(	const double	nu,
		const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	mu,
		const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &	s,
		RNG &	rng
	)

inline

Definition at line 184 of file multi_student_t.hpp.

template<bool propto, typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::multinomial_log	(	const std::vector< int > &	ns,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta
	)

Definition at line 25 of file multinomial.hpp.

template<typename T_prob >

boost::math::tools::promote_args<T_prob>::type stan::prob::multinomial_log	(	const std::vector< int > &	ns,
		const Eigen::Matrix< T_prob, Eigen::Dynamic, 1 > &	theta
	)

Definition at line 61 of file multinomial.hpp.

template<class RNG >

std::vector<int> stan::prob::multinomial_rng	(	const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	theta,
		const int	N,
		RNG &	rng
	)

inline

Definition at line 68 of file multinomial.hpp.

template<bool propto, typename T_n , typename T_location , typename T_inv_scale >

return_type<T_location, T_inv_scale>::type stan::prob::neg_binomial_2_log	(	const T_n &	n,
		const T_location &	mu,
		const T_inv_scale &	phi
	)

Definition at line 31 of file neg_binomial_2.hpp.

template<typename T_n , typename T_location , typename T_inv_scale >

return_type<T_location, T_inv_scale>::type stan::prob::neg_binomial_2_log	(	const T_n &	n,
		const T_location &	mu,
		const T_inv_scale &	phi
	)

inline

Definition at line 138 of file neg_binomial_2.hpp.

template<bool propto, typename T_n , typename T_log_location , typename T_inv_scale >

return_type<T_log_location, T_inv_scale>::type stan::prob::neg_binomial_2_log_log	(	const T_n &	n,
		const T_log_location &	eta,
		const T_inv_scale &	phi
	)

Definition at line 150 of file neg_binomial_2.hpp.

template<typename T_n , typename T_log_location , typename T_inv_scale >

return_type<T_log_location, T_inv_scale>::type stan::prob::neg_binomial_2_log_log	(	const T_n &	n,
		const T_log_location &	eta,
		const T_inv_scale &	phi
	)

inline

Definition at line 258 of file neg_binomial_2.hpp.

template<class RNG >

int stan::prob::neg_binomial_2_log_rng	(	const double	eta,
		const double	phi,
		RNG &	rng
	)

inline

Definition at line 286 of file neg_binomial_2.hpp.

template<class RNG >

int stan::prob::neg_binomial_2_rng	(	const double	mu,
		const double	phi,
		RNG &	rng
	)

inline

Definition at line 266 of file neg_binomial_2.hpp.

template<typename T_n , typename T_shape , typename T_inv_scale >

return_type<T_shape, T_inv_scale>::type stan::prob::neg_binomial_ccdf_log	(	const T_n &	n,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

Definition at line 428 of file neg_binomial.hpp.

template<typename T_n , typename T_shape , typename T_inv_scale >

return_type<T_shape, T_inv_scale>::type stan::prob::neg_binomial_cdf	(	const T_n &	n,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

Definition at line 181 of file neg_binomial.hpp.

template<typename T_n , typename T_shape , typename T_inv_scale >

return_type<T_shape, T_inv_scale>::type stan::prob::neg_binomial_cdf_log	(	const T_n &	n,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

Definition at line 314 of file neg_binomial.hpp.

template<bool propto, typename T_n , typename T_shape , typename T_inv_scale >

return_type<T_shape, T_inv_scale>::type stan::prob::neg_binomial_log	(	const T_n &	n,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

Definition at line 30 of file neg_binomial.hpp.

template<typename T_n , typename T_shape , typename T_inv_scale >

return_type<T_shape, T_inv_scale>::type stan::prob::neg_binomial_log	(	const T_n &	n,
		const T_shape &	alpha,
		const T_inv_scale &	beta
	)

inline

Definition at line 171 of file neg_binomial.hpp.

template<class RNG >

int stan::prob::neg_binomial_rng	(	const double	alpha,
		const double	beta,
		RNG &	rng
	)

inline

Definition at line 541 of file neg_binomial.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::normal_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 305 of file normal.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::normal_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Calculates the normal cumulative distribution function for the given variate, location, and scale.

$\Phi(x) = \frac{1}{\sqrt{2 \pi}} \int_{-\inf}^x e^{-t^2/2} dt$ .

Errors are configured by policy. All variables must be finite and the scale must be strictly greater than zero.

Parameters

y	A scalar variate.
mu	The location of the normal distribution.
sigma	The scale of the normal distriubtion

Returns: The unit normal cdf evaluated at the specified arguments.

Template Parameters

T_y	Type of y.
T_loc	Type of mean parameter.
T_scale	Type of standard deviation paramater.
Policy	Error-handling policy.

Definition at line 152 of file normal.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::normal_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 233 of file normal.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

boost::enable_if_c<contains_fvar<T_y,T_loc,T_scale>::value, typename return_type<T_y,T_loc,T_scale>::type>::type stan::prob::normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 22 of file normal.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

boost::enable_if_c<is_var_or_arithmetic<T_y,T_loc,T_scale>::value, typename return_type<T_y,T_loc,T_scale>::type>::type stan::prob::normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s).

y, mu, or sigma can each be either a scalar or a std::vector. Any vector inputs must be the same length.

The result log probability is defined to be the sum of the log probabilities for each observation/mean/deviation triple.

Parameters

y	(Sequence of) scalar(s).
mu	(Sequence of) location parameter(s) for the normal distribution.
sigma	(Sequence of) scale parameters for the normal distribution.

Returns: The log of the product of the densities.

Exceptions

std::domain_error if the scale is not positive.

Template Parameters

T_y	Underlying type of scalar in sequence.
T_loc	Type of location parameter.

Definition at line 41 of file normal.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma
	)

inline

Definition at line 128 of file normal.hpp.

template<class RNG >

double stan::prob::normal_rng	(	const double	mu,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 377 of file normal.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::ordered_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & x )

Return an increasing ordered vector derived from the specified free vector.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters

x	Free vector of scalars.

Returns: Positive, increasing ordered vector.

Template Parameters

T	Type of scalar.

Definition at line 1224 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::ordered_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		T &	lp
	)

inline

Return a positive valued, increasing ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters

x	Free vector of scalars.
lp	Log probability reference.

Returns: Positive, increasing ordered vector.

Template Parameters

T	Type of scalar.

Definition at line 1256 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::ordered_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & y )

Return the vector of unconstrained scalars that transform to the specified positive ordered vector.

This function inverts the constraining operation defined in ordered_constrain(Matrix),

Parameters

y	Vector of positive, ordered scalars.

Returns: Free vector that transforms into the input vector.

Template Parameters

T	Type of scalar.

Exceptions

std::domain_error if y is not a vector of positive, ordered scalars.

Definition at line 1285 of file transform.hpp.

template<bool propto, typename T_lambda , typename T_cut >

boost::math::tools::promote_args<T_lambda,T_cut>::type stan::prob::ordered_logistic_log	(	int	y,
		const T_lambda &	lambda,
		const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &	c
	)

Returns the (natural) log probability of the specified integer outcome given the continuous location and specified cutpoints in an ordered logistic model.

Typically the continous location will be the dot product of a vector of regression coefficients and a vector of predictors for the outcome.

Template Parameters

propto	True if calculating up to a proportion.
T_loc	Location type.
T_cut	Cut-point type.
Policy	Error policy (only its type matters).

Parameters

y	Outcome.
lambda	Location.
c	Positive increasing vector of cutpoints.

Returns: Log probability of outcome given location and cutpoints.

Exceptions

std::domain_error If the outcome is not between 1 and the number of cutpoints plus 2; if the cutpoint vector is empty; if the cutpoint vector contains a non-positive, non-finite value; or if the cutpoint vector is not sorted in ascending order.

Definition at line 60 of file ordered_logistic.hpp.

template<typename T_lambda , typename T_cut >

boost::math::tools::promote_args<T_lambda,T_cut>::type stan::prob::ordered_logistic_log	(	int	y,
		const T_lambda &	lambda,
		const Eigen::Matrix< T_cut, Eigen::Dynamic, 1 > &	c
	)

Definition at line 108 of file ordered_logistic.hpp.

template<class RNG >

int stan::prob::ordered_logistic_rng	(	const double	eta,
		const Eigen::Matrix< double, Eigen::Dynamic, 1 > &	c,
		RNG &	rng
	)

inline

Definition at line 115 of file ordered_logistic.hpp.

template<typename T_y , typename T_scale , typename T_shape >

return_type<T_y, T_scale, T_shape>::type stan::prob::pareto_ccdf_log	(	const T_y &	y,
		const T_scale &	y_min,
		const T_shape &	alpha
	)

Definition at line 303 of file pareto.hpp.

template<typename T_y , typename T_scale , typename T_shape >

return_type<T_y, T_scale, T_shape>::type stan::prob::pareto_cdf	(	const T_y &	y,
		const T_scale &	y_min,
		const T_shape &	alpha
	)

Definition at line 128 of file pareto.hpp.

template<typename T_y , typename T_scale , typename T_shape >

return_type<T_y, T_scale, T_shape>::type stan::prob::pareto_cdf_log	(	const T_y &	y,
		const T_scale &	y_min,
		const T_shape &	alpha
	)

Definition at line 223 of file pareto.hpp.

template<bool propto, typename T_y , typename T_scale , typename T_shape >

return_type<T_y,T_scale,T_shape>::type stan::prob::pareto_log	(	const T_y &	y,
		const T_scale &	y_min,
		const T_shape &	alpha
	)

Definition at line 24 of file pareto.hpp.

template<typename T_y , typename T_scale , typename T_shape >

return_type<T_y,T_scale,T_shape>::type stan::prob::pareto_log	(	const T_y &	y,
		const T_scale &	y_min,
		const T_shape &	alpha
	)

inline

Definition at line 122 of file pareto.hpp.

template<class RNG >

double stan::prob::pareto_rng	(	const double	y_min,
		const double	alpha,
		RNG &	rng
	)

inline

Definition at line 379 of file pareto.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y, T_loc, T_scale, T_shape>::type stan::prob::pareto_type_2_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	lambda,
		const T_shape &	alpha
	)

Definition at line 381 of file pareto_type_2.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y, T_loc, T_scale, T_shape>::type stan::prob::pareto_type_2_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	lambda,
		const T_shape &	alpha
	)

Definition at line 140 of file pareto_type_2.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y, T_loc, T_scale, T_shape>::type stan::prob::pareto_type_2_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	lambda,
		const T_shape &	alpha
	)

Definition at line 270 of file pareto_type_2.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y,T_loc,T_scale,T_shape>::type stan::prob::pareto_type_2_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	lambda,
		const T_shape &	alpha
	)

Definition at line 24 of file pareto_type_2.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y,T_loc,T_scale,T_shape>::type stan::prob::pareto_type_2_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	lambda,
		const T_shape &	alpha
	)

inline

Definition at line 133 of file pareto_type_2.hpp.

template<class RNG >

double stan::prob::pareto_type_2_rng	(	const double	mu,
		const double	lambda,
		const double	alpha,
		RNG &	rng
	)

inline

Definition at line 495 of file pareto_type_2.hpp.

template<typename T_n , typename T_rate >

return_type<T_rate>::type stan::prob::poisson_ccdf_log	(	const T_n &	n,
		const T_rate &	lambda
	)

Definition at line 322 of file poisson.hpp.

template<typename T_n , typename T_rate >

return_type<T_rate>::type stan::prob::poisson_cdf	(	const T_n &	n,
		const T_rate &	lambda
	)

Definition at line 194 of file poisson.hpp.

template<typename T_n , typename T_rate >

return_type<T_rate>::type stan::prob::poisson_cdf_log	(	const T_n &	n,
		const T_rate &	lambda
	)

Definition at line 260 of file poisson.hpp.

template<bool propto, typename T_n , typename T_rate >

return_type<T_rate>::type stan::prob::poisson_log	(	const T_n &	n,
		const T_rate &	lambda
	)

Definition at line 27 of file poisson.hpp.

template<typename T_n , typename T_rate >

return_type<T_rate>::type stan::prob::poisson_log	(	const T_n &	n,
		const T_rate &	lambda
	)

inline

Definition at line 101 of file poisson.hpp.

template<bool propto, typename T_n , typename T_log_rate >

return_type<T_log_rate>::type stan::prob::poisson_log_log	(	const T_n &	n,
		const T_log_rate &	alpha
	)

Definition at line 109 of file poisson.hpp.

template<typename T_n , typename T_log_rate >

return_type<T_log_rate>::type stan::prob::poisson_log_log	(	const T_n &	n,
		const T_log_rate &	alpha
	)

inline

Definition at line 187 of file poisson.hpp.

template<class RNG >

int stan::prob::poisson_rng	(	const double	lambda,
		RNG &	rng
	)

inline

Definition at line 384 of file poisson.hpp.

template<typename T >

T stan::prob::positive_constrain ( const T x )

inline

Return the positive value for the specified unconstrained input.

The transform applied is

$f(x) = \exp(x)$ .

Parameters

x	Arbitrary input scalar.

Returns: Input transformed to be positive.

Definition at line 446 of file transform.hpp.

template<typename T >

T stan::prob::positive_constrain	(	const T	x,
		T &	lp
	)

inline

Return the positive value for the specified unconstrained input, incrementing the scalar reference with the log absolute Jacobian determinant.

See positive_constrain(T) for details of the transform. The log absolute Jacobian determinant is

$\log | \frac{d}{dx} \mbox{exp}(x) | = \log | \mbox{exp}(x) | = x$ .

Parameters

x	Arbitrary input scalar.
lp	Log probability reference.

Returns: Input transformed to be positive.

Template Parameters

T	Type of scalar.

Definition at line 468 of file transform.hpp.

template<typename T >

T stan::prob::positive_free ( const T y )

inline

Return the unconstrained value corresponding to the specified positive-constrained value.

The transform is the inverse of the transform $f$ applied by positive_constrain(T), namely

$f^{-1}(x) = \log(x)$ .

The input is validated using stan::math::check_positive().

Parameters

y	Input scalar.

Returns: Unconstrained value that produces the input when constrained.

Template Parameters

T	Type of scalar.

Exceptions

std::domain_error if the variable is negative.

Definition at line 491 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::positive_ordered_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & x )

Return an increasing positive ordered vector derived from the specified free vector.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters

x	Free vector of scalars.

Returns: Positive, increasing ordered vector.

Template Parameters

T	Type of scalar.

Definition at line 1317 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::positive_ordered_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	x,
		T &	lp
	)

inline

Return a positive valued, increasing positive ordered vector derived from the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The returned constrained vector will have the same dimensionality as the specified free vector.

Parameters

x	Free vector of scalars.
lp	Log probability reference.

Returns: Positive, increasing ordered vector.

Template Parameters

T	Type of scalar.

Definition at line 1348 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::positive_ordered_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & y )

Return the vector of unconstrained scalars that transform to the specified positive ordered vector.

This function inverts the constraining operation defined in positive_ordered_constrain(Matrix),

Parameters

y	Vector of positive, ordered scalars.

Returns: Free vector that transforms into the input vector.

Template Parameters

T	Type of scalar.

Exceptions

std::domain_error if y is not a vector of positive, ordered scalars.

Definition at line 1376 of file transform.hpp.

template<typename T >

T stan::prob::prob_constrain ( const T x )

inline

Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar.

The transform is the inverse logit,

$f(x) = \mbox{logit}^{-1}(x) = \frac{1}{1 + \exp(x)}$ .

Parameters

x	Free scalar.

Returns: Probability-constrained result of transforming the free scalar.

Template Parameters

T	Type of scalar.

Definition at line 875 of file transform.hpp.

template<typename T >

T stan::prob::prob_constrain	(	const T	x,
		T &	lp
	)

inline

Return a probability value constrained to fall between 0 and 1 (inclusive) for the specified free scalar and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The transform is as defined for prob_constrain(T). The log absolute Jacobian determinant is

The log absolute Jacobian determinant is

$\log | \frac{d}{dx} \mbox{logit}^{-1}(x) |$

$\log ((\mbox{logit}^{-1}(x)) (1 - \mbox{logit}^{-1}(x))$

$\log (\mbox{logit}^{-1}(x)) + \log (1 - \mbox{logit}^{-1}(x))$ .

Parameters

x	Free scalar.
lp	Log probability reference.

Returns: Probability-constrained result of transforming the free scalar.

Template Parameters

T	Type of scalar.

Definition at line 903 of file transform.hpp.

template<typename T >

T stan::prob::prob_free ( const T y )

inline

Return the free scalar that when transformed to a probability produces the specified scalar.

The function that reverses the constraining transform specified in prob_constrain(T) is the logit function,

$f^{-1}(y) = \mbox{logit}(y) = \frac{1 - y}{y}$ .

Parameters

y	Scalar input.

Template Parameters

T	Type of scalar.

Exceptions

std::domain_error if y is less than 0 or greater than 1.

Definition at line 927 of file transform.hpp.

template<typename T_y , typename T_scale >

return_type<T_y,T_scale>::type stan::prob::rayleigh_ccdf_log	(	const T_y &	y,
		const T_scale &	sigma
	)

Definition at line 239 of file rayleigh.hpp.

template<typename T_y , typename T_scale >

return_type<T_y,T_scale>::type stan::prob::rayleigh_cdf	(	const T_y &	y,
		const T_scale &	sigma
	)

Definition at line 105 of file rayleigh.hpp.

template<typename T_y , typename T_scale >

return_type<T_y,T_scale>::type stan::prob::rayleigh_cdf_log	(	const T_y &	y,
		const T_scale &	sigma
	)

Definition at line 176 of file rayleigh.hpp.

template<bool propto, typename T_y , typename T_scale >

return_type<T_y,T_scale>::type stan::prob::rayleigh_log	(	const T_y &	y,
		const T_scale &	sigma
	)

Definition at line 21 of file rayleigh.hpp.

template<typename T_y , typename T_scale >

return_type<T_y,T_scale>::type stan::prob::rayleigh_log	(	const T_y &	y,
		const T_scale &	sigma
	)

inline

Definition at line 99 of file rayleigh.hpp.

template<class RNG >

double stan::prob::rayleigh_rng	(	const double	sigma,
		RNG &	rng
	)

inline

Definition at line 299 of file rayleigh.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::read_corr_L	(	const Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		const size_t	K
	)

Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations.

It is generally better to work with the Cholesky factor rather than the correlation matrix itself when the determinant, inverse, etc. of the correlation matrix is needed for some statistical calculation.

See read_corr_matrix(Array,size_t,T) for more information.

Parameters

CPCs	The (K choose 2) canonical partial correlations in (-1,1).
K	Dimensionality of correlation matrix.

Returns: Cholesky factor of correlation matrix for specified canonical partial correlations.

Template Parameters

T	Type of underlying scalar.

Definition at line 139 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::read_corr_L	(	const Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		const size_t	K,
		T &	log_prob
	)

Return the Cholesky factor of the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation.

The implementation is Ben Goodrich's Cholesky factor-based approach to the C-vine method of:

Daniel Lewandowski, Dorota Kurowicka, and Harry Joe, Generating random correlation matrices based on vines and extended onion method Journal of Multivariate Analysis 100 (2009) 1989–2001

Parameters

CPCs	The (K choose 2) canonical partial correlations in (-1,1).
K	Dimensionality of correlation matrix.
log_prob	Reference to variable to increment with the log Jacobian determinant.

Returns: Cholesky factor of correlation matrix for specified partial correlations.

Template Parameters

T	Type of underlying scalar.

Definition at line 215 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::read_corr_matrix	(	const Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		const size_t	K
	)

Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations.

See read_corr_matrix(Array,size_t,T) for more information.

Parameters

CPCs	The (K choose 2) canonical partial correlations in (-1,1).
K	Dimensionality of correlation matrix.

Returns: Cholesky factor of correlation matrix for specified canonical partial correlations.

Template Parameters

T	Type of underlying scalar.

Definition at line 181 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::read_corr_matrix	(	const Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		const size_t	K,
		T &	log_prob
	)

Return the correlation matrix of the specified dimensionality corresponding to the specified canonical partial correlations, incrementing the specified scalar reference with the log absolute determinant of the Jacobian of the transformation.

It is usually preferable to utilize the version that returns the Cholesky factor of the correlation matrix rather than the correlation matrix itself in statistical calculations.

Parameters

CPCs	The (K choose 2) canonical partial correlations in (-1,1).
K	Dimensionality of correlation matrix.
log_prob	Reference to variable to increment with the log Jacobian determinant.

Returns: Correlation matrix for specified partial correlations.

Template Parameters

T	Type of underlying scalar.

Definition at line 258 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::read_cov_L	(	const Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		const Eigen::Array< T, Eigen::Dynamic, 1 > &	sds,
		T &	log_prob
	)

This is the function that should be called prior to evaluating the density of any elliptical distribution.

Parameters

CPCs	on (-1,1)
sds	on (0,inf)
log_prob	the log probability value to increment with the Jacobian

Returns: Cholesky factor of covariance matrix for specified partial correlations.

Definition at line 280 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::read_cov_matrix	(	const Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		const Eigen::Array< T, Eigen::Dynamic, 1 > &	sds,
		T &	log_prob
	)

A generally worse alternative to call prior to evaluating the density of an elliptical distribution.

Parameters

CPCs	on (-1,1)
sds	on (0,inf)
log_prob	the log probability value to increment with the Jacobian

Returns: Covariance matrix for specified partial correlations.

Definition at line 300 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,Eigen::Dynamic> stan::prob::read_cov_matrix	(	const Eigen::Array< T, Eigen::Dynamic, 1 > &	CPCs,
		const Eigen::Array< T, Eigen::Dynamic, 1 > &	sds
	)

Builds a covariance matrix from CPCs and standard deviations.

Parameters

CPCs	in (-1,1)
sds	in (0,inf)

Definition at line 319 of file transform.hpp.

template<typename T_y , typename T_dof , typename T_scale >

return_type<T_y, T_dof, T_scale>::type stan::prob::scaled_inv_chi_square_ccdf_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_scale &	s
	)

Definition at line 419 of file scaled_inv_chi_square.hpp.

template<typename T_y , typename T_dof , typename T_scale >

return_type<T_y, T_dof, T_scale>::type stan::prob::scaled_inv_chi_square_cdf	(	const T_y &	y,
		const T_dof &	nu,
		const T_scale &	s
	)

The CDF of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.

Parameters

y	A scalar variable.
nu	Degrees of freedom.
s	Scale parameter.

Exceptions

std::domain_error	if nu is not greater than 0
std::domain_error	if s is not greater than 0.
std::domain_error	if y is not greater than 0.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.

Definition at line 187 of file scaled_inv_chi_square.hpp.

template<typename T_y , typename T_dof , typename T_scale >

return_type<T_y, T_dof, T_scale>::type stan::prob::scaled_inv_chi_square_cdf_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_scale &	s
	)

Definition at line 310 of file scaled_inv_chi_square.hpp.

template<bool propto, typename T_y , typename T_dof , typename T_scale >

return_type<T_y,T_dof,T_scale>::type stan::prob::scaled_inv_chi_square_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_scale &	s
	)

The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.

$\begin{eqnarray*} y &\sim& \mbox{\sf{Inv-}}\chi^2(\nu, s^2) \\ \log (p (y \,|\, \nu, s)) &=& \log \left( \frac{(\nu / 2)^{\nu / 2}}{\Gamma (\nu / 2)} s^\nu y^{- (\nu / 2 + 1)} \exp^{-\nu s^2 / (2y)} \right) \\ &=& \frac{\nu}{2} \log(\frac{\nu}{2}) - \log (\Gamma (\nu / 2)) + \nu \log(s) - (\frac{\nu}{2} + 1) \log(y) - \frac{\nu s^2}{2y} \\ & & \mathrm{ where } \; y > 0 \end{eqnarray*}$

Parameters

y	A scalar variable.
nu	Degrees of freedom.
s	Scale parameter.

Exceptions

std::domain_error	if nu is not greater than 0
std::domain_error	if s is not greater than 0.
std::domain_error	if y is not greater than 0.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.

Definition at line 44 of file scaled_inv_chi_square.hpp.

template<typename T_y , typename T_dof , typename T_scale >

return_type<T_y,T_dof,T_scale>::type stan::prob::scaled_inv_chi_square_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_scale &	s
	)

inline

Definition at line 167 of file scaled_inv_chi_square.hpp.

template<class RNG >

double stan::prob::scaled_inv_chi_square_rng	(	const double	nu,
		const double	s,
		RNG &	rng
	)

inline

Definition at line 528 of file scaled_inv_chi_square.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::simplex_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & y )

Return the simplex corresponding to the specified free vector.

A simplex is a vector containing values greater than or equal to 0 that sum to 1. A vector with (K-1) unconstrained values will produce a simplex of size K.

The transform is based on a centered stick-breaking process.

Parameters

y	Free vector input of dimensionality K - 1.

Returns: Simplex of dimensionality K.

Template Parameters

T	Type of scalar.

Definition at line 1103 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::simplex_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	y,
		T &	lp
	)

Return the simplex corresponding to the specified free vector and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The simplex transform is defined through a centered stick-breaking process.

Parameters

y	Free vector input of dimensionality K - 1.
lp	Log probability reference to increment.

Returns: Simplex of dimensionality K.

Template Parameters

T	Type of scalar.

Definition at line 1142 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::simplex_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & x )

Return an unconstrained vector that when transformed produces the specified simplex.

It applies to a simplex of dimensionality K and produces an unconstrained vector of dimensionality (K-1).

The simplex transform is defined through a centered stick-breaking process.

Parameters

x	Simplex of dimensionality K.

Returns: Free vector of dimensionality (K-1) that transfroms to the simplex.

Template Parameters

T	Type of scalar.

Exceptions

std::domain_error if x is not a valid simplex

Definition at line 1188 of file transform.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y,T_loc,T_scale,T_shape>::type stan::prob::skew_normal_ccdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_shape &	alpha
	)

Definition at line 320 of file skew_normal.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y,T_loc,T_scale,T_shape>::type stan::prob::skew_normal_cdf	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_shape &	alpha
	)

Definition at line 141 of file skew_normal.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y,T_loc,T_scale,T_shape>::type stan::prob::skew_normal_cdf_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_shape &	alpha
	)

Definition at line 237 of file skew_normal.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y,T_loc,T_scale,T_shape>::type stan::prob::skew_normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_shape &	alpha
	)

Definition at line 23 of file skew_normal.hpp.

template<typename T_y , typename T_loc , typename T_scale , typename T_shape >

return_type<T_y,T_loc,T_scale, T_shape>::type stan::prob::skew_normal_log	(	const T_y &	y,
		const T_loc &	mu,
		const T_scale &	sigma,
		const T_shape &	alpha
	)

inline

Definition at line 134 of file skew_normal.hpp.

template<class RNG >

double stan::prob::skew_normal_rng	(	const double	mu,
		const double	sigma,
		const double	alpha,
		RNG &	rng
	)

inline

Definition at line 403 of file skew_normal.hpp.

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >

return_type<T_y, T_dof, T_loc, T_scale>::type stan::prob::student_t_ccdf_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 555 of file student_t.hpp.

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >

return_type<T_y, T_dof, T_loc, T_scale>::type stan::prob::student_t_cdf	(	const T_y &	y,
		const T_dof &	nu,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 219 of file student_t.hpp.

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >

return_type<T_y, T_dof, T_loc, T_scale>::type stan::prob::student_t_cdf_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_loc &	mu,
		const T_scale &	sigma
	)

Definition at line 393 of file student_t.hpp.

template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >

return_type<T_y,T_dof,T_loc,T_scale>::type stan::prob::student_t_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_loc &	mu,
		const T_scale &	sigma
	)

The log of the Student-t density for the given y, nu, mean, and scale parameter.

The scale parameter must be greater than 0.

$\begin{eqnarray*} y &\sim& t_{\nu} (\mu, \sigma^2) \\ \log (p (y \,|\, \nu, \mu, \sigma) ) &=& \log \left( \frac{\Gamma((\nu + 1) /2)} {\Gamma(\nu/2)\sqrt{\nu \pi} \sigma} \left( 1 + \frac{1}{\nu} (\frac{y - \mu}{\sigma})^2 \right)^{-(\nu + 1)/2} \right) \\ &=& \log( \Gamma( (\nu+1)/2 )) - \log (\Gamma (\nu/2) - \frac{1}{2} \log(\nu \pi) - \log(\sigma) -\frac{\nu + 1}{2} \log (1 + \frac{1}{\nu} (\frac{y - \mu}{\sigma})^2) \end{eqnarray*}$

Parameters

y	A scalar variable.
nu	Degrees of freedom.
mu	The mean of the Student-t distribution.
sigma	The scale parameter of the Student-t distribution.

Returns: The log of the Student-t density at y.

Exceptions

std::domain_error	if sigma is not greater than 0.
std::domain_error	if nu is not greater than 0.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.
T_loc	Type of location.
T_scale	Type of scale.

Definition at line 49 of file student_t.hpp.

template<typename T_y , typename T_dof , typename T_loc , typename T_scale >

return_type<T_y,T_dof,T_loc,T_scale>::type stan::prob::student_t_log	(	const T_y &	y,
		const T_dof &	nu,
		const T_loc &	mu,
		const T_scale &	sigma
	)

inline

Definition at line 212 of file student_t.hpp.

template<class RNG >

double stan::prob::student_t_rng	(	const double	nu,
		const double	mu,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 717 of file student_t.hpp.

template<typename T , typename TU >

boost::math::tools::promote_args<T,TU>::type stan::prob::ub_constrain	(	const T	x,
		const TU	ub
	)

inline

Return the upper-bounded value for the specified unconstrained scalar and upper bound.

The transform is

$f(x) = U - \exp(x)$

where $U$ is the upper bound.

If the upper bound is positive infinity, this function reduces to identity_constrain(x).

Parameters

x	Free scalar.
ub	Upper bound.

Returns: Transformed scalar with specified upper bound.

Template Parameters

T	Type of scalar.
TU	Type of upper bound.

Definition at line 604 of file transform.hpp.

template<typename T , typename TU >

boost::math::tools::promote_args<T,TU>::type stan::prob::ub_constrain	(	const T	x,
		const TU	ub,
		T &	lp
	)

inline

Return the upper-bounded value for the specified unconstrained scalar and upper bound and increment the specified log probability reference with the log absolute Jacobian determinant of the transform.

The transform is as specified for ub_constrain(T,double). The log absolute Jacobian determinant is

$\log | \frac{d}{dx} -\mbox{exp}(x) + U | = \log | -\mbox{exp}(x) + 0 | = x$ .

If the upper bound is positive infinity, this function reduces to identity_constrain(x,lp).

Parameters

x	Free scalar.
ub	Upper bound.
lp	Log probability reference.

Returns: Transformed scalar with specified upper bound.

Template Parameters

T	Type of scalar.
TU	Type of upper bound.

Definition at line 636 of file transform.hpp.

template<typename T , typename TU >

boost::math::tools::promote_args<T,TU>::type stan::prob::ub_free	(	const T	y,
		const TU	ub
	)

inline

Return the free scalar that corresponds to the specified upper-bounded value with respect to the specified upper bound.

The transform is the reverse of the ub_constrain(T,double) transform,

$f^{-1}(y) = \log -(y - U)$

where $U$ is the upper bound.

If the upper bound is positive infinity, this function reduces to identity_free(y).

Parameters

y	Upper-bounded scalar.
ub	Upper bound.

Returns: Free scalar corresponding to upper-bounded scalar.

Template Parameters

T	Type of scalar.
TU	Type of upper bound.

Exceptions

std::invalid_argument if y is greater than the upper bound.

Definition at line 668 of file transform.hpp.

template<typename T_y , typename T_low , typename T_high >

return_type<T_y,T_low,T_high>::type stan::prob::uniform_ccdf_log	(	const T_y &	y,
		const T_low &	alpha,
		const T_high &	beta
	)

Definition at line 270 of file uniform.hpp.

template<typename T_y , typename T_low , typename T_high >

return_type<T_y,T_low,T_high>::type stan::prob::uniform_cdf	(	const T_y &	y,
		const T_low &	alpha,
		const T_high &	beta
	)

Definition at line 125 of file uniform.hpp.

template<typename T_y , typename T_low , typename T_high >

return_type<T_y,T_low,T_high>::type stan::prob::uniform_cdf_log	(	const T_y &	y,
		const T_low &	alpha,
		const T_high &	beta
	)

Definition at line 201 of file uniform.hpp.

template<bool propto, typename T_y , typename T_low , typename T_high >

return_type<T_y,T_low,T_high>::type stan::prob::uniform_log	(	const T_y &	y,
		const T_low &	alpha,
		const T_high &	beta
	)

The log of a uniform density for the given y, lower, and upper bound.

$\begin{eqnarray*} y &\sim& \mbox{\sf{U}}(\alpha, \beta) \\ \log (p (y \,|\, \alpha, \beta)) &=& \log \left( \frac{1}{\beta-\alpha} \right) \\ &=& \log (1) - \log (\beta - \alpha) \\ &=& -\log (\beta - \alpha) \\ & & \mathrm{ where } \; y \in [\alpha, \beta], \log(0) \; \mathrm{otherwise} \end{eqnarray*}$

Parameters

y	A scalar variable.
alpha	Lower bound.
beta	Upper bound.

Exceptions

std::invalid_argument if the lower bound is greater than or equal to the lower bound

Template Parameters

T_y	Type of scalar.
T_low	Type of lower bound.
T_high	Type of upper bound.

Definition at line 44 of file uniform.hpp.

template<typename T_y , typename T_low , typename T_high >

return_type<T_y,T_low,T_high>::type stan::prob::uniform_log	(	const T_y &	y,
		const T_low &	alpha,
		const T_high &	beta
	)

inline

Definition at line 119 of file uniform.hpp.

template<class RNG >

double stan::prob::uniform_rng	(	const double	alpha,
		const double	beta,
		RNG &	rng
	)

inline

Definition at line 339 of file uniform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::unit_vector_constrain ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & y )

Return the unit length vector corresponding to the free vector y.

The free vector contains K-1 spherical coordinates.

Parameters

y	of K - 1 spherical coordinates

Returns: Unit length vector of dimension K

Template Parameters

T	Scalar type.

Definition at line 1015 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::unit_vector_constrain	(	const Eigen::Matrix< T, Eigen::Dynamic, 1 > &	y,
		T &	lp
	)

Return the unit length vector corresponding to the free vector y.

The free vector contains K-1 spherical coordinates.

Parameters

y	of K - 1 spherical coordinates

Returns: Unit length vector of dimension K

Parameters

lp	Log probability reference to increment.

Template Parameters

T	Scalar type.

Definition at line 1044 of file transform.hpp.

template<typename T >

Eigen::Matrix<T,Eigen::Dynamic,1> stan::prob::unit_vector_free ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > & x )

Definition at line 1067 of file transform.hpp.

template<bool propto, typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::von_mises_log	(	T_y const &	y,
		T_loc const &	mu,
		T_scale const &	kappa
	)

Definition at line 19 of file von_mises.hpp.

template<typename T_y , typename T_loc , typename T_scale >

return_type<T_y,T_loc,T_scale>::type stan::prob::von_mises_log	(	T_y const &	y,
		T_loc const &	mu,
		T_scale const &	kappa
	)

inline

Definition at line 115 of file von_mises.hpp.

template<class RNG >

double stan::prob::von_mises_rng	(	const double	mu,
		const double	kappa,
		RNG &	rng
	)

inline

Definition at line 130 of file von_mises.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::weibull_ccdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 254 of file weibull.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::weibull_cdf	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 138 of file weibull.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::weibull_cdf_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 201 of file weibull.hpp.

template<bool propto, typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::weibull_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

Definition at line 24 of file weibull.hpp.

template<typename T_y , typename T_shape , typename T_scale >

return_type<T_y,T_shape,T_scale>::type stan::prob::weibull_log	(	const T_y &	y,
		const T_shape &	alpha,
		const T_scale &	sigma
	)

inline

Definition at line 132 of file weibull.hpp.

template<class RNG >

double stan::prob::weibull_rng	(	const double	alpha,
		const double	sigma,
		RNG &	rng
	)

inline

Definition at line 304 of file weibull.hpp.

template<bool propto, typename T_y , typename T_dof , typename T_scale >

boost::math::tools::promote_args<T_y,T_dof,T_scale>::type stan::prob::wishart_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const T_dof &	nu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &	S
	)

The log of the Wishart density for the given W, degrees of freedom, and scale matrix.

The scale matrix, S, must be k x k, symmetric, and semi-positive definite. Dimension, k, is implicit. nu must be greater than k-1

$\begin{eqnarray*} W &\sim& \mbox{\sf{Wishart}}_{\nu} (S) \\ \log (p (W \,|\, \nu, S) ) &=& \log \left( \left(2^{\nu k/2} \pi^{k (k-1) /4} \prod_{i=1}^k{\Gamma (\frac{\nu + 1 - i}{2})} \right)^{-1} \times \left| S \right|^{-\nu/2} \left| W \right|^{(\nu - k - 1) / 2} \times \exp (-\frac{1}{2} \mbox{tr} (S^{-1} W)) \right) \\ &=& -\frac{\nu k}{2}\log(2) - \frac{k (k-1)}{4} \log(\pi) - \sum_{i=1}^{k}{\log (\Gamma (\frac{\nu+1-i}{2}))} -\frac{\nu}{2} \log(\det(S)) + \frac{\nu-k-1}{2}\log (\det(W)) - \frac{1}{2} \mbox{tr} (S^{-1}W) \end{eqnarray*}$

Parameters

W	A scalar matrix
nu	Degrees of freedom
S	The scale matrix

Returns: The log of the Wishart density at W given nu and S.

Exceptions

std::domain_error	if nu is not greater than k-1
std::domain_error	if S is not square, not symmetric, or not semi-positive definite.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.
T_scale	Type of scale.

Definition at line 62 of file wishart.hpp.

template<typename T_y , typename T_dof , typename T_scale >

boost::math::tools::promote_args<T_y,T_dof,T_scale>::type stan::prob::wishart_log	(	const Eigen::Matrix< T_y, Eigen::Dynamic, Eigen::Dynamic > &	W,
		const T_dof &	nu,
		const Eigen::Matrix< T_scale, Eigen::Dynamic, Eigen::Dynamic > &	S
	)

inline

Definition at line 135 of file wishart.hpp.

template<class RNG >

Eigen::Matrix<double, Eigen::Dynamic, Eigen::Dynamic> stan::prob::wishart_rng	(	const double	nu,
		const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &	S,
		RNG &	rng
	)

inline

Definition at line 143 of file wishart.hpp.

Variable Documentation

const double stan::prob::CONSTRAINT_TOLERANCE = 1E-8

Definition at line 32 of file transform.hpp.

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Variable Documentation