Multivariate Distributions

Detailed Description

Distributions with Matrix inputs.

Functions
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta >
return_type_t< T_x, T_alpha, T_beta >	stan::math::bernoulli_logit_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta)
template<typename T_y , typename T_x , typename T_alpha , typename T_beta >
return_type_t< T_x, T_alpha, T_beta >	stan::math::bernoulli_logit_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta)
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta , require_matrix_t< T_x > * = nullptr>
return_type_t< T_x, T_alpha, T_beta >	stan::math::bernoulli_logit_glm_lpmf (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta)
	Returns the log PMF of the Generalized Linear Model (GLM) with Bernoulli distribution and logit link function.
template<typename T_x , typename T_alpha , typename T_beta , class RNG >
VectorBuilder< true, int, T_alpha >::type	stan::math::bernoulli_logit_glm_rng (const T_x &x, const T_alpha &alpha, const T_beta &beta, RNG &rng)
	Returns a draw from the Generalized Linear Model (GLM) with Bernoulli distribution and logit link function.
template<bool propto, typename T_n , typename T_prob >
return_type_t< T_prob >	stan::math::categorical_log (const T_n &ns, const T_prob &theta)
template<typename T_n , typename T_prob >
return_type_t< T_prob >	stan::math::categorical_log (const T_n &ns, const T_prob &theta)
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta , require_matrix_t< T_x > * = nullptr, require_col_vector_t< T_alpha > * = nullptr, require_matrix_t< T_beta > * = nullptr>
return_type_t< T_x, T_alpha, T_beta >	stan::math::categorical_logit_glm_lpmf (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta)
	Returns the log PMF of the Generalized Linear Model (GLM) with categorical distribution and logit (softmax) link function.
template<bool propto, typename T_n , typename T_prob >
return_type_t< T_prob >	stan::math::categorical_logit_log (const T_n &ns, const T_prob &beta)
template<typename T_n , typename T_prob >
return_type_t< T_prob >	stan::math::categorical_logit_log (const T_n &ns, const T_prob &beta)
template<class RNG >
int	stan::math::categorical_logit_rng (const Eigen::VectorXd &beta, RNG &rng)
	Return a draw from a Categorical distribution given a a vector of unnormalized log probabilities and a psuedo-random number generator.
template<bool propto, typename T_prob , typename T_prior_size >
return_type_t< T_prob, T_prior_size >	stan::math::dirichlet_log (const T_prob &theta, const T_prior_size &alpha)
	The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha.
template<typename T_prob , typename T_prior_size >
return_type_t< T_prob, T_prior_size >	stan::math::dirichlet_log (const T_prob &theta, const T_prior_size &alpha)
template<bool propto, typename T_prob , typename T_prior_size , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_prob, T_prior_size > * = nullptr>
return_type_t< T_prob, T_prior_size >	stan::math::dirichlet_lpdf (const T_prob &theta, const T_prior_size &alpha)
	The log of the Dirichlet density for the given theta and a vector of prior sample sizes, alpha.
template<bool propto, typename T_prob , typename T_prior_size >
return_type_t< T_prob, T_prior_size >	stan::math::dirichlet_lpmf (const T_prob &theta, const T_prior_size &alpha)
template<bool propto, typename T_prior_size , require_eigen_col_vector_t< T_prior_size > * = nullptr>
return_type_t< T_prior_size >	stan::math::dirichlet_multinomial_lpmf (const std::vector< int > &ns, const T_prior_size &alpha)
	The log of the Dirichlet-Multinomial probability for the given integer vector \(n\) and a vector of prior sample sizes, \(\alpha\).
template<class RNG >
std::vector< int >	stan::math::dirichlet_multinomial_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &alpha, int N, RNG &rng)
	Return a draw from a Dirichlet-Multinomial distribution with specified parameters \(\alpha\) and \(N\) and pseudo-random number generator rng.
template<class RNG >
Eigen::VectorXd	stan::math::dirichlet_rng (const Eigen::Matrix< double, Eigen::Dynamic, 1 > &alpha, RNG &rng)
	Return a draw from a Dirichlet distribution with specified parameters and pseudo-random number generator.
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< T_y, T_F, T_G, T_V, T_W, T_m0, T_C0 >	stan::math::gaussian_dlm_obs_log (const T_y &y, const T_F &F, const T_G &G, const T_V &V, const T_W &W, const T_m0 &m0, const T_C0 &C0)
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< T_y, T_F, T_G, T_V, T_W, T_m0, T_C0 >	stan::math::gaussian_dlm_obs_log (const T_y &y, const T_F &F, const T_G &G, const T_V &V, const T_W &W, const T_m0 &m0, const T_C0 &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 , require_all_eigen_matrix_dynamic_t< T_y, T_F, T_G, T_V, T_W, T_C0 > * = nullptr, require_eigen_col_vector_t< T_m0 > * = nullptr>
return_type_t< T_y, T_F, T_G, T_V, T_W, T_m0, T_C0 >	stan::math::gaussian_dlm_obs_lpdf (const T_y &y, const T_F &F, const T_G &G, const T_V &V, const T_W &W, const T_m0 &m0, const T_C0 &C0)
	The log of a Gaussian dynamic linear model (GDLM).
template<class RNG >
Eigen::VectorXd	stan::math::internal::multi_normal_semidefinite_rng (const Eigen::VectorXd &mu, const Eigen::LDLT< Eigen::MatrixXd > &S_ldlt, RNG &rng)
	Return a multivariate normal random variate with the given location and covariance using the specified random number generator.
template<class RNG >
Eigen::MatrixXd	stan::math::gaussian_dlm_obs_rng (const Eigen::MatrixXd &F, const Eigen::MatrixXd &G, const Eigen::MatrixXd &V, const Eigen::MatrixXd &W, const Eigen::VectorXd &m0, const Eigen::MatrixXd &C0, const int T, RNG &rng)
	Simulate random draw from Gaussian dynamic linear model (GDLM).
template<bool propto, typename T_y , typename T_dof , typename T_scale , require_stan_scalar_t< T_dof > * = nullptr, require_all_matrix_t< T_y, T_scale > * = nullptr>
return_type_t< T_y, T_dof, T_scale >	stan::math::inv_wishart_cholesky_lpdf (const T_y &L_Y, const T_dof &nu, const T_scale &L_S)
	Return the natural logarithm of the unnormalized inverse wishart density of the specified lower-triangular Cholesky factor variate, positive degrees of freedom, and lower-triangular Cholesky factor of the scale matrix.
template<class RNG >
Eigen::MatrixXd	stan::math::inv_wishart_cholesky_rng (double nu, const Eigen::MatrixXd &L_S, RNG &rng)
	Return a random Cholesky factor of a covariance matrix of the specified dimensionality drawn from the inverse Wishart distribution with the specified degrees of freedom using the specified random number generator.
template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type_t< T_y, T_dof, T_scale >	stan::math::inv_wishart_log (const T_y &W, const T_dof &nu, const T_scale &S)
	The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix.
template<typename T_y , typename T_dof , typename T_scale >
return_type_t< T_y, T_dof, T_scale >	stan::math::inv_wishart_log (const T_y &W, const T_dof &nu, const T_scale &S)
template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type_t< T_y, T_dof, T_scale >	stan::math::inv_wishart_lpdf (const T_y &W, const T_dof &nu, const T_scale &S)
	The log of the Inverse-Wishart density for the given W, degrees of freedom, and scale matrix.
template<bool propto, typename T_covar , typename T_shape >
return_type_t< T_covar, T_shape >	stan::math::lkj_corr_cholesky_log (const T_covar &L, const T_shape &eta)
template<typename T_covar , typename T_shape >
return_type_t< T_covar, T_shape >	stan::math::lkj_corr_cholesky_log (const T_covar &L, const T_shape &eta)
template<bool propto, typename T_y , typename T_shape >
return_type_t< T_y, T_shape >	stan::math::lkj_corr_log (const T_y &y, const T_shape &eta)
template<typename T_y , typename T_shape >
return_type_t< T_y, T_shape >	stan::math::lkj_corr_log (const T_y &y, const T_shape &eta)
template<class RNG >
Eigen::MatrixXd	stan::math::lkj_corr_rng (size_t K, double eta, RNG &rng)
	Return a random correlation matrix (symmetric, positive definite, unit diagonal) of the specified dimensionality drawn from the LKJ distribution with the specified degrees of freedom using the specified random number generator.
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_shape >
return_type_t< T_y, T_loc, T_scale, T_shape >	stan::math::lkj_cov_log (const T_y &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 >
return_type_t< T_y, T_loc, T_scale, T_shape >	stan::math::lkj_cov_log (const T_y &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 , require_all_matrix_t< T_y, T_Mu, T_Sigma, T_D > * = nullptr>
return_type_t< T_y, T_Mu, T_Sigma, T_D >	stan::math::matrix_normal_prec_log (const T_y &y, const T_Mu &Mu, const T_Sigma &Sigma, const T_D &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.
template<typename T_y , typename T_Mu , typename T_Sigma , typename T_D , require_all_matrix_t< T_y, T_Mu, T_Sigma, T_D > * = nullptr>
return_type_t< T_y, T_Mu, T_Sigma, T_D >	stan::math::matrix_normal_prec_log (const T_y &y, const T_Mu &Mu, const T_Sigma &Sigma, const T_D &D)
template<bool propto, typename T_y , typename T_Mu , typename T_Sigma , typename T_D , require_all_matrix_t< T_y, T_Mu, T_Sigma, T_D > * = nullptr>
return_type_t< T_y, T_Mu, T_Sigma, T_D >	stan::math::matrix_normal_prec_lpdf (const T_y &y, const T_Mu &Mu, const T_Sigma &Sigma, const T_D &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.
template<class RNG >
Eigen::MatrixXd	stan::math::matrix_normal_prec_rng (const Eigen::MatrixXd &Mu, const Eigen::MatrixXd &Sigma, const Eigen::MatrixXd &D, RNG &rng)
	Sample from the the matrix normal distribution for the given Mu, Sigma and D where Sigma and D are given as precision matrices, not covariance matrices.
template<bool propto, typename T_y , typename T_covar , typename T_w >
return_type_t< T_y, T_covar, T_w >	stan::math::multi_gp_cholesky_log (const T_y &y, const T_covar &L, const T_w &w)
	The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma.
template<typename T_y , typename T_covar , typename T_w >
return_type_t< T_y, T_covar, T_w >	stan::math::multi_gp_cholesky_log (const T_y &y, const T_covar &L, const T_w &w)
template<bool propto, typename T_y , typename T_covar , typename T_w , require_all_eigen_matrix_dynamic_t< T_y, T_covar > * = nullptr, require_eigen_col_vector_t< T_w > * = nullptr>
return_type_t< T_y, T_covar, T_w >	stan::math::multi_gp_cholesky_lpdf (const T_y &y, const T_covar &L, const T_w &w)
	The log of a multivariate Gaussian Process for the given y, w, and a Cholesky factor L of the kernel matrix Sigma.
template<bool propto, typename T_y , typename T_covar , typename T_w >
return_type_t< T_y, T_covar, T_w >	stan::math::multi_gp_log (const T_y &y, const T_covar &Sigma, const T_w &w)
	The log of a multivariate Gaussian Process for the given y, Sigma, and w.
template<typename T_y , typename T_covar , typename T_w >
return_type_t< T_y, T_covar, T_w >	stan::math::multi_gp_log (const T_y &y, const T_covar &Sigma, const T_w &w)
template<bool propto, typename T_y , typename T_covar , typename T_w , require_all_matrix_t< T_y, T_covar > * = nullptr, require_col_vector_t< T_w > * = nullptr>
return_type_t< T_y, T_covar, T_w >	stan::math::multi_gp_lpdf (const T_y &y, const T_covar &Sigma, const T_w &w)
	The log of a multivariate Gaussian Process for the given y, Sigma, and w.
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type_t< T_y, T_loc, T_covar >	stan::math::multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const T_covar &L)
	The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix.
template<typename T_y , typename T_loc , typename T_covar >
return_type_t< T_y, T_loc, T_covar >	stan::math::multi_normal_cholesky_log (const T_y &y, const T_loc &mu, const T_covar &L)
template<bool propto, typename T_y , typename T_loc , typename T_covar , require_any_not_vector_vt< is_stan_scalar, T_y, T_loc > * = nullptr, require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_covar > * = nullptr>
return_type_t< T_y, T_loc, T_covar >	stan::math::multi_normal_cholesky_lpdf (const T_y &y, const T_loc &mu, const T_covar &L)
	The log of the multivariate normal density for the given y, mu, and a Cholesky factor L of the variance matrix.
template<typename T_loc , class RNG >
StdVectorBuilder< true, Eigen::VectorXd, T_loc >::type	stan::math::multi_normal_cholesky_rng (const T_loc &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &L, RNG &rng)
	Return a multivariate normal random variate with the given location and Cholesky factorization of the covariance using the specified random number generator.
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type_t< T_y, T_loc, T_covar >	stan::math::multi_normal_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
template<typename T_y , typename T_loc , typename T_covar >
return_type_t< T_y, T_loc, T_covar >	stan::math::multi_normal_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
template<bool propto, typename T_y , typename T_loc , typename T_covar >
return_type_t< T_y, T_loc, T_covar >	stan::math::multi_normal_prec_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
template<typename T_y , typename T_loc , typename T_covar >
return_type_t< T_y, T_loc, T_covar >	stan::math::multi_normal_prec_log (const T_y &y, const T_loc &mu, const T_covar &Sigma)
template<typename T_loc , class RNG >
StdVectorBuilder< true, Eigen::VectorXd, T_loc >::type	stan::math::multi_normal_prec_rng (const T_loc &mu, const Eigen::MatrixXd &S, RNG &rng)
	Return a multivariate normal random variate with the given location and precision using the specified random number generator.
template<typename T_loc , class RNG >
StdVectorBuilder< true, Eigen::VectorXd, T_loc >::type	stan::math::multi_normal_rng (const T_loc &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng)
	Return a multivariate normal random variate with the given location and covariance using the specified random number generator.
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_covar , require_any_not_vector_vt< is_stan_scalar, T_y, T_dof, T_loc > * = nullptr, require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_covar > * = nullptr>
return_type_t< T_y, T_dof, T_loc, T_covar >	stan::math::multi_student_t_cholesky_lpdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_covar &L)
	The log of the multivariate student t density for the given y, mu, nu, and a Cholesky factor L of the scale matrix.
template<typename T_loc , class RNG >
StdVectorBuilder< true, Eigen::VectorXd, T_loc >::type	stan::math::multi_student_t_cholesky_rng (double nu, const T_loc &mu, const Eigen::MatrixXd &L, RNG &rng)
	Return a multivariate student-t random variate with the given degrees of freedom location and Cholesky factor the scale matrix using the specified random number generator.
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type_t< T_y, T_dof, T_loc, T_scale >	stan::math::multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
	Return the log of the multivariate Student t distribution at the specified arguments.
template<typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type_t< T_y, T_dof, T_loc, T_scale >	stan::math::multi_student_t_log (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
template<bool propto, typename T_y , typename T_dof , typename T_loc , typename T_scale >
return_type_t< T_y, T_dof, T_loc, T_scale >	stan::math::multi_student_t_lpdf (const T_y &y, const T_dof &nu, const T_loc &mu, const T_scale &Sigma)
	The log of the multivariate student t density for the given y, mu, nu, and scale matrix.
template<typename T_loc , class RNG >
StdVectorBuilder< true, Eigen::VectorXd, T_loc >::type	stan::math::multi_student_t_rng (double nu, const T_loc &mu, const Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic > &S, RNG &rng)
	Return a multivariate student-t random variate with the given degrees of freedom location and Cholesky factor the scale matrix using the specified random number generator.
template<bool propto, typename T_prob >
return_type_t< T_prob >	stan::math::multinomial_log (const std::vector< int > &ns, const T_prob &theta)
template<typename T_prob >
return_type_t< T_prob >	stan::math::multinomial_log (const std::vector< int > &ns, const T_prob &theta)
template<bool propto, typename T_beta , require_eigen_col_vector_t< T_beta > * = nullptr>
return_type_t< T_beta >	stan::math::multinomial_logit_log (const std::vector< int > &ns, const T_beta &beta)
template<typename T_beta , require_eigen_col_vector_t< T_beta > * = nullptr>
return_type_t< T_beta >	stan::math::multinomial_logit_log (const std::vector< int > &ns, const T_beta &beta)
template<bool propto, typename T_beta , typename T_prob = scalar_type_t<T_beta>, require_eigen_col_vector_t< T_beta > * = nullptr>
return_type_t< T_prob >	stan::math::multinomial_logit_lpmf (const std::vector< int > &ns, const T_beta &beta)
	Multinomial log PMF in log parametrization.
template<class RNG , typename T_beta , require_eigen_col_vector_t< T_beta > * = nullptr>
std::vector< int >	stan::math::multinomial_logit_rng (const T_beta &beta, int N, RNG &rng)
	Return a draw from a Multinomial distribution given a a vector of unnormalized log probabilities and a pseudo-random number generator.
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta , typename T_precision >
return_type_t< T_x, T_alpha, T_beta, T_precision >	stan::math::neg_binomial_2_log_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta, const T_precision &phi)
template<typename T_y , typename T_x , typename T_alpha , typename T_beta , typename T_precision >
return_type_t< T_x, T_alpha, T_beta, T_precision >	stan::math::neg_binomial_2_log_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta, const T_precision &phi)
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta , typename T_precision , require_matrix_t< T_x > * = nullptr>
return_type_t< T_x, T_alpha, T_beta, T_precision >	stan::math::neg_binomial_2_log_glm_lpmf (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta, const T_precision &phi)
	Returns the log PMF of the Generalized Linear Model (GLM) with Negative-Binomial-2 distribution and log link function.
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta , typename T_scale >
return_type_t< T_y, T_x, T_alpha, T_beta, T_scale >	stan::math::normal_id_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta, const T_scale &sigma)
template<typename T_y , typename T_x , typename T_alpha , typename T_beta , typename T_scale >
return_type_t< T_y, T_x, T_alpha, T_beta, T_scale >	stan::math::normal_id_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta, const T_scale &sigma)
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta , typename T_scale , require_matrix_t< T_x > * = nullptr>
return_type_t< T_y, T_x, T_alpha, T_beta, T_scale >	stan::math::normal_id_glm_lpdf (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta, const T_scale &sigma)
	Returns the log PDF of the Generalized Linear Model (GLM) with Normal distribution and id link function.
template<bool propto, typename T_y , typename T_x , typename T_beta , typename T_cuts , require_matrix_t< T_x > * = nullptr, require_all_col_vector_t< T_beta, T_cuts > * = nullptr>
return_type_t< T_x, T_beta, T_cuts >	stan::math::ordered_logistic_glm_lpmf (const T_y &y, const T_x &x, const T_beta &beta, const T_cuts &cuts)
	Returns the log PMF of the ordinal regression Generalized Linear Model (GLM).
template<bool propto, typename T_y , typename T_loc , typename T_cut >
return_type_t< T_loc, T_cut >	stan::math::ordered_logistic_log (const T_y &y, const T_loc &lambda, const T_cut &c)
	Returns the (natural) log probability of the integer/s given the vector of continuous location/s and specified cutpoints in an ordered logistic model.
template<typename T_y , typename T_loc , typename T_cut >
return_type_t< T_loc, T_cut >	stan::math::ordered_logistic_log (const T_y &y, const T_loc &lambda, const T_cut &c)
template<bool propto, typename T_y , typename T_loc , typename T_cut , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_cut > * = nullptr>
return_type_t< T_loc, T_cut >	stan::math::ordered_logistic_lpmf (const T_y &y, const T_loc &lambda, const T_cut &c)
	Returns the (natural) log probability of the specified array of integers given the vector of continuous locations and specified cutpoints in an ordered logistic model.
template<bool propto, typename T_y , typename T_loc , typename T_cut >
return_type_t< T_loc, T_cut >	stan::math::ordered_probit_log (const T_y &y, const T_loc &lambda, const T_cut &c)
	Returns the (natural) log probability of the integer/s given the vector of continuous location/s and specified cutpoints in an ordered probit model.
template<typename T_y , typename T_loc , typename T_cut >
return_type_t< T_loc, T_cut >	stan::math::ordered_probit_log (const T_y &y, const T_loc &lambda, const T_cut &c)
template<bool propto, typename T_y , typename T_loc , typename T_cut >
return_type_t< T_loc, T_cut >	stan::math::ordered_probit_lpmf (const T_y &y, const T_loc &lambda, const T_cut &c)
	Returns the (natural) log probability of the specified array of integers given the vector of continuous locations and array of specified cutpoints in an ordered probit model.
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta >
return_type_t< T_x, T_alpha, T_beta >	stan::math::poisson_log_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta)
template<typename T_y , typename T_x , typename T_alpha , typename T_beta >
return_type_t< T_x, T_alpha, T_beta >	stan::math::poisson_log_glm_log (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta)
template<bool propto, typename T_y , typename T_x , typename T_alpha , typename T_beta , require_matrix_t< T_x > * = nullptr>
return_type_t< T_x, T_alpha, T_beta >	stan::math::poisson_log_glm_lpmf (const T_y &y, const T_x &x, const T_alpha &alpha, const T_beta &beta)
	Returns the log PMF of the Generalized Linear Model (GLM) with Poisson distribution and log link function.
template<bool propto, typename T_y , typename T_dof , typename T_scale , require_stan_scalar_t< T_dof > * = nullptr, require_all_matrix_t< T_y, T_scale > * = nullptr>
return_type_t< T_y, T_dof, T_scale >	stan::math::wishart_cholesky_lpdf (const T_y &L_Y, const T_dof &nu, const T_scale &L_S)
	Return the natural logarithm of the unnormalized Wishart density of the specified lower-triangular Cholesky factor variate, positive degrees of freedom, and lower-triangular Cholesky factor of the scale matrix.
template<class RNG >
Eigen::MatrixXd	stan::math::wishart_cholesky_rng (double nu, const Eigen::MatrixXd &L_S, RNG &rng)
	Return a random Cholesky factor of the inverse covariance matrix of the specified dimensionality drawn from the Wishart distribution with the specified degrees of freedom using the specified random number generator.
template<bool propto, typename T_y , typename T_dof , typename T_scale >
return_type_t< T_y, T_dof, T_scale >	stan::math::wishart_log (const T_y &W, const T_dof &nu, const T_scale &S)
	The log of the Wishart density for the given W, degrees of freedom, and scale matrix.
template<typename T_y , typename T_dof , typename T_scale >
return_type_t< T_y, T_dof, T_scale >	stan::math::wishart_log (const T_y &W, const T_dof &nu, const T_scale &S)
template<bool propto, typename T_y , typename T_dof , typename T_scale , require_stan_scalar_t< T_dof > * = nullptr, require_all_matrix_t< T_y, T_scale > * = nullptr>
return_type_t< T_y, T_dof, T_scale >	stan::math::wishart_lpdf (const T_y &W, const T_dof &nu, const T_scale &S)
	The log of the Wishart density for the given W, degrees of freedom, and scale matrix.