Probability Distributions

Detailed Description

Modules
	Multivariate Distributions
	Distributions with Matrix inputs.
	Univariate Distributions
	Distributions with scalar, vector, or array input.

Functions
template<typename T_n_cl , typename T_prob_cl , require_all_prim_or_rev_kernel_expression_t< T_n_cl, T_prob_cl > * = nullptr, require_any_not_stan_scalar_t< T_n_cl, T_prob_cl > * = nullptr>
return_type_t< T_prob_cl >	stan::math::bernoulli_cdf (const T_n_cl &n, const T_prob_cl &theta)
	Returns the CDF of the Bernoulli distribution.
template<typename T_n_cl , typename T_prob_cl , require_all_prim_or_rev_kernel_expression_t< T_n_cl, T_prob_cl > * = nullptr, require_any_not_stan_scalar_t< T_n_cl, T_prob_cl > * = nullptr>
return_type_t< T_prob_cl >	stan::math::bernoulli_lccdf (const T_n_cl &n, const T_prob_cl &theta)
	Returns the log CCDF of the Bernoulli distribution.
template<typename T_n_cl , typename T_prob_cl , require_all_prim_or_rev_kernel_expression_t< T_n_cl, T_prob_cl > * = nullptr, require_any_not_stan_scalar_t< T_n_cl, T_prob_cl > * = nullptr>
return_type_t< T_prob_cl >	stan::math::bernoulli_lcdf (const T_n_cl &n, const T_prob_cl &theta)
	Returns the log CDF of the Bernoulli distribution.
template<bool propto, typename T_n_cl , typename T_prob_cl , require_all_prim_or_rev_kernel_expression_t< T_n_cl, T_prob_cl > * = nullptr, require_any_not_stan_scalar_t< T_n_cl, T_prob_cl > * = nullptr>
return_type_t< T_prob_cl >	stan::math::bernoulli_logit_lpmf (const T_n_cl &n, const T_prob_cl &theta)
	Returns the log PMF of the logit-parametrized Bernoulli distribution.
template<typename T_n , typename T_prob >
return_type_t< T_prob >	stan::math::bernoulli_ccdf_log (const T_n &n, const T_prob &theta)
template<typename T_n , typename T_prob , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_prob > * = nullptr>
return_type_t< T_prob >	stan::math::bernoulli_cdf (const T_n &n, const T_prob &theta)
	Returns the CDF of the Bernoulli distribution.
template<typename T_n , typename T_prob >
return_type_t< T_prob >	stan::math::bernoulli_cdf_log (const T_n &n, const T_prob &theta)
template<typename T_n , typename T_prob , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_prob > * = nullptr>
return_type_t< T_prob >	stan::math::bernoulli_lccdf (const T_n &n, const T_prob &theta)
	Returns the log CCDF of the Bernoulli distribution.
template<typename T_n , typename T_prob , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_prob > * = nullptr>
return_type_t< T_prob >	stan::math::bernoulli_lcdf (const T_n &n, const T_prob &theta)
	Returns the log CDF of the Bernoulli distribution.
template<bool propto, typename T_n , typename T_prob , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_prob > * = nullptr>
return_type_t< T_prob >	stan::math::bernoulli_logit_lpmf (const T_n &n, const T_prob &theta)
	Returns the log PMF of the logit-parametrized Bernoulli distribution.
template<typename T_t , class RNG >
VectorBuilder< true, int, T_t >::type	stan::math::bernoulli_logit_rng (const T_t &t, RNG &rng)
	Return a Bernoulli random variate with logit-parameterized chance of success using the specified random number generator.
template<bool propto, typename T_n , typename T_prob , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_prob > * = nullptr>
return_type_t< T_prob >	stan::math::bernoulli_lpmf (const T_n &n, const T_prob &theta)
	Returns the log PMF of the Bernoulli distribution.
template<typename T_theta , class RNG >
VectorBuilder< true, int, T_theta >::type	stan::math::bernoulli_rng (const T_theta &theta, RNG &rng)
	Return a Bernoulli random variate with specified chance of success parameter using the specified random number generator.
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type_t< T_size1, T_size2 >	stan::math::beta_binomial_ccdf_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< T_size1, T_size2 >	stan::math::beta_binomial_cdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
	Returns the CDF of the Beta-Binomial distribution with given population size, prior success, and prior failure parameters.
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type_t< T_size1, T_size2 >	stan::math::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< T_size1, T_size2 >	stan::math::beta_binomial_lccdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
	Returns the log CCDF of the Beta-Binomial distribution with given population size, prior success, and prior failure parameters.
template<typename T_n , typename T_N , typename T_size1 , typename T_size2 >
return_type_t< T_size1, T_size2 >	stan::math::beta_binomial_lcdf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
	Returns the log CDF of the Beta-Binomial distribution with given population size, prior success, and prior failure parameters.
template<bool propto, typename T_n , typename T_N , typename T_size1 , typename T_size2 , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_N, T_size1, T_size2 > * = nullptr>
return_type_t< T_size1, T_size2 >	stan::math::beta_binomial_lpmf (const T_n &n, const T_N &N, const T_size1 &alpha, const T_size2 &beta)
	Returns the log PMF of the Beta-Binomial distribution with given population size, prior success, and prior failure parameters.
template<typename T_N , typename T_shape1 , typename T_shape2 , class RNG >
VectorBuilder< true, int, T_N, T_shape1, T_shape2 >::type	stan::math::beta_binomial_rng (const T_N &N, const T_shape1 &alpha, const T_shape2 &beta, RNG &rng)
	Return a beta-binomial random variate with the specified population size, success, and failure parameters using the given random number generator.
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type_t< T_y, T_scale_succ, T_scale_fail >	stan::math::beta_ccdf_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< T_y, T_scale_succ, T_scale_fail >	stan::math::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.
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type_t< T_y, T_scale_succ, T_scale_fail >	stan::math::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< T_y, T_scale_succ, T_scale_fail >	stan::math::beta_lccdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta_param)
	Returns the beta log complementary cumulative distribution function for the given probability, success, and failure parameters.
template<typename T_y , typename T_scale_succ , typename T_scale_fail >
return_type_t< T_y, T_scale_succ, T_scale_fail >	stan::math::beta_lcdf (const T_y &y, const T_scale_succ &alpha, const T_scale_fail &beta_param)
	Returns the beta log cumulative distribution function for the given probability, success, and failure parameters.
template<bool propto, typename T_y , typename T_scale_succ , typename T_scale_fail , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_scale_succ, T_scale_fail > * = nullptr>
return_type_t< T_y, T_scale_succ, T_scale_fail >	stan::math::beta_lpdf (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 stan::math::size(s).
template<typename T_n , typename T_r , typename T_alpha , typename T_beta >
return_type_t< T_r, T_alpha, T_beta >	stan::math::beta_neg_binomial_cdf (const T_n &n, const T_r &r, const T_alpha &alpha, const T_beta &beta, const double precision=1e-8, const int max_steps=1e8)
	Returns the CDF of the Beta-Negative Binomial distribution with given number of successes, prior success, and prior failure parameters.
template<typename T_n , typename T_r , typename T_alpha , typename T_beta >
return_type_t< T_r, T_alpha, T_beta >	stan::math::beta_neg_binomial_lccdf (const T_n &n, const T_r &r, const T_alpha &alpha, const T_beta &beta, const double precision=1e-8, const int max_steps=1e8)
	Returns the log CCDF of the Beta-Negative Binomial distribution with given number of successes, prior success, and prior failure parameters.
template<typename T_n , typename T_r , typename T_alpha , typename T_beta >
return_type_t< T_r, T_alpha, T_beta >	stan::math::beta_neg_binomial_lcdf (const T_n &n, const T_r &r, const T_alpha &alpha, const T_beta &beta, const double precision=1e-8, const int max_steps=1e8)
	Returns the log CDF of the Beta-Negative Binomial distribution with given number of successes, prior success, and prior failure parameters.
template<bool propto, typename T_n , typename T_r , typename T_alpha , typename T_beta , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_r, T_alpha, T_beta > * = nullptr>
return_type_t< T_r, T_alpha, T_beta >	stan::math::beta_neg_binomial_lpmf (const T_n &n, const T_r &r, const T_alpha &alpha, const T_beta &beta)
	Returns the log PMF of the Beta Negative Binomial distribution with given number of successes, prior success, and prior failure parameters.
template<typename T_r , typename T_alpha , typename T_beta , typename RNG >
auto	stan::math::beta_neg_binomial_rng (const T_r &r, const T_alpha &alpha, const T_beta &beta, RNG &rng)
	Return a beta-negative binomial random variate with the given number of successes, prior success, and prior failure parameters, using the given random number generator.
template<typename T_y , typename T_loc , typename T_prec >
return_type_t< T_y, T_loc, T_prec >	stan::math::beta_proportion_ccdf_log (const T_y &y, const T_loc &mu, const T_prec &kappa)
template<typename T_y , typename T_loc , typename T_prec >
return_type_t< T_y, T_loc, T_prec >	stan::math::beta_proportion_cdf_log (const T_y &y, const T_loc &mu, const T_prec &kappa)
template<typename T_y , typename T_loc , typename T_prec >
return_type_t< T_y, T_loc, T_prec >	stan::math::beta_proportion_lccdf (const T_y &y, const T_loc &mu, const T_prec &kappa)
	Returns the beta log complementary cumulative distribution function for specified probability, location, and precision parameters: beta_proportion_lccdf(y | mu, kappa) = beta_lccdf(y | mu * kappa, (1 - mu) * kappa).
template<typename T_y , typename T_loc , typename T_prec >
return_type_t< T_y, T_loc, T_prec >	stan::math::beta_proportion_lcdf (const T_y &y, const T_loc &mu, const T_prec &kappa)
	Returns the beta log cumulative distribution function for specified probability, location, and precision parameters: beta_proportion_lcdf(y | mu, kappa) = beta_lcdf(y | mu * kappa, (1 - mu) * kappa).
template<bool propto, typename T_y , typename T_loc , typename T_prec , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_prec > * = nullptr>
return_type_t< T_y, T_loc, T_prec >	stan::math::beta_proportion_lpdf (const T_y &y, const T_loc &mu, const T_prec &kappa)
	The log of the beta density for specified y, location, and precision: beta_proportion_lpdf(y | mu, kappa) = beta_lpdf(y | mu * kappa, (1 - mu) * kappa).
template<typename T_loc , typename T_prec , class RNG >
VectorBuilder< true, double, T_loc, T_prec >::type	stan::math::beta_proportion_rng (const T_loc &mu, const T_prec &kappa, RNG &rng)
	Return a Beta random variate specified probability, location, and precision parameters: beta_proportion_rng(y | mu, kappa) = beta_rng(y | mu * kappa, (1 - mu) * kappa).
template<typename T_shape1 , typename T_shape2 , class RNG >
VectorBuilder< true, double, T_shape1, T_shape2 >::type	stan::math::beta_rng (const T_shape1 &alpha, const T_shape2 &beta, RNG &rng)
	Return a Beta random variate with the supplied success and failure parameters using the given random number generator.
template<typename T_n , typename T_N , typename T_prob >
return_type_t< T_prob >	stan::math::binomial_ccdf_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< T_prob >	stan::math::binomial_cdf (const T_n &n, const T_N &N, const T_prob &theta)
	Returns the CDF for the binomial distribution evaluated at the specified success, population size, and chance of success.
template<typename T_n , typename T_N , typename T_prob >
return_type_t< T_prob >	stan::math::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< T_prob >	stan::math::binomial_lccdf (const T_n &n, const T_N &N, const T_prob &theta)
	Returns the log CCDF for the binomial distribution evaluated at the specified success, population size, and chance of success.
template<typename T_n , typename T_N , typename T_prob >
return_type_t< T_prob >	stan::math::binomial_lcdf (const T_n &n, const T_N &N, const T_prob &theta)
	Returns the log CDF for the binomial distribution evaluated at the specified success, population size, and chance of success.
template<bool propto, typename T_n , typename T_N , 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::binomial_logit_glm_lpmf (const T_n &n, const T_N &N, const T_x &x, const T_alpha &alpha, const T_beta &beta)
	Returns the log PMF of the Generalized Linear Model (GLM) with Binomial distribution and logit link function.
template<bool propto, typename T_n , typename T_N , typename T_prob , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_N, T_prob > * = nullptr>
return_type_t< T_prob >	stan::math::binomial_logit_lpmf (const T_n &n, const T_N &N, const T_prob &alpha)
	Binomial log PMF in logit parametrization.
template<bool propto, typename T_n , typename T_N , typename T_prob , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_n, T_N, T_prob > * = nullptr>
return_type_t< T_prob >	stan::math::binomial_lpmf (const T_n &n, const T_N &N, const T_prob &theta)
	Returns the log PMF for the binomial distribution evaluated at the specified success, population size, and chance of success.
template<typename T_N , typename T_theta , class RNG >
VectorBuilder< true, int, T_N, T_theta >::type	stan::math::binomial_rng (const T_N &N, const T_theta &theta, RNG &rng)
	Return a pseudorandom binomial random variable for the given population size and chance of success parameters using the specified random number generator.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::cauchy_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
template<typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::cauchy_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Returns the cauchy cumulative distribution function for the given location, and scale.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::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 , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::cauchy_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Returns the cauchy log complementary cumulative distribution function for the given location, and scale.
template<typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::cauchy_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Returns the cauchy log cumulative distribution function for the given location, and scale.
template<bool propto, typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::cauchy_lpdf (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).
template<typename T_loc , typename T_scale , class RNG >
VectorBuilder< true, double, T_loc, T_scale >::type	stan::math::cauchy_rng (const T_loc &mu, const T_scale &sigma, RNG &rng)
	Return a Cauchy random variate for the given location and scale using the specified random number generator.
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::chi_square_ccdf_log (const T_y &y, const T_dof &nu)
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::chi_square_cdf (const T_y &y, const T_dof &nu)
	Returns the chi square cumulative distribution function for the given variate and degrees of freedom.
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::chi_square_cdf_log (const T_y &y, const T_dof &nu)
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::chi_square_lccdf (const T_y &y, const T_dof &nu)
	Returns the chi square log complementary cumulative distribution function for the given variate and degrees of freedom.
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::chi_square_lcdf (const T_y &y, const T_dof &nu)
	Returns the chi square log cumulative distribution function for the given variate and degrees of freedom.
template<bool propto, typename T_y , typename T_dof , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_dof > * = nullptr>
return_type_t< T_y, T_dof >	stan::math::chi_square_lpdf (const T_y &y, const T_dof &nu)
	The log of a chi-squared density for y with the specified degrees of freedom parameter.
template<typename T_deg , class RNG >
VectorBuilder< true, double, T_deg >::type	stan::math::chi_square_rng (const T_deg &nu, RNG &rng)
	Return a chi squared random variate with nu degrees of freedom using the specified random number generator.
template<typename T_y , typename T_lower , typename T_upper >
double	stan::math::discrete_range_ccdf_log (const T_y &y, const T_lower &lower, const T_upper &upper)
template<typename T_y , typename T_lower , typename T_upper >
double	stan::math::discrete_range_cdf (const T_y &y, const T_lower &lower, const T_upper &upper)
	Return the CDF of a discrete range distribution for the given y, lower and upper bounds (all integers).
template<typename T_y , typename T_lower , typename T_upper >
double	stan::math::discrete_range_cdf_log (const T_y &y, const T_lower &lower, const T_upper &upper)
template<typename T_y , typename T_lower , typename T_upper >
double	stan::math::discrete_range_lccdf (const T_y &y, const T_lower &lower, const T_upper &upper)
	Return the log CCDF of a discrete range distribution for the given y, lower and upper bounds (all integers).
template<typename T_y , typename T_lower , typename T_upper >
double	stan::math::discrete_range_lcdf (const T_y &y, const T_lower &lower, const T_upper &upper)
	Return the log CDF of a discrete range distribution for the given y, lower and upper bounds (all integers).
template<bool propto, typename T_y , typename T_lower , typename T_upper >
double	stan::math::discrete_range_lpmf (const T_y &y, const T_lower &lower, const T_upper &upper)
	Return the log PMF of a discrete range for the given y, lower and upper bound (all integers).
template<typename T_lower , typename T_upper , class RNG >
VectorBuilder< true, int, T_lower, T_upper >::type	stan::math::discrete_range_rng (const T_lower &lower, const T_upper &upper, RNG &rng)
	Return an integer random variate between the given lower and upper bounds (inclusive) using the specified random number generator.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::double_exponential_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
template<typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::double_exponential_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Returns the double exponential cumulative density function.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::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 , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::double_exponential_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Returns the double exponential log complementary cumulative density function.
template<typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::double_exponential_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Returns the double exponential log cumulative density function.
template<bool propto, typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::double_exponential_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma)
	Returns the double exponential log probability density function.
template<typename T_loc , typename T_scale , class RNG >
VectorBuilder< true, double, T_loc, T_scale >::type	stan::math::double_exponential_rng (const T_loc &mu, const T_scale &sigma, RNG &rng)
	Return a double exponential random variate with the given location and scale using the specified random number generator.
template<typename T_y , typename T_loc , typename T_scale , typename T_inv_scale >
return_type_t< T_y, T_loc, T_scale, T_inv_scale >	stan::math::exp_mod_normal_ccdf_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< T_y, T_loc, T_scale, T_inv_scale >	stan::math::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_loc , typename T_scale , typename T_inv_scale , class RNG >
VectorBuilder< true, double, T_loc, T_scale, T_inv_scale >::type	stan::math::exp_mod_normal_rng (const T_loc &mu, const T_scale &sigma, const T_inv_scale &lambda, RNG &rng)
	Return an exponentially modified normal random variate for the given location, scale, and inverse scale using the specified random number generator.
template<typename T_y , typename T_inv_scale >
return_type_t< T_y, T_inv_scale >	stan::math::exponential_ccdf_log (const T_y &y, const T_inv_scale &beta)
template<typename T_y , typename T_inv_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_inv_scale > * = nullptr>
return_type_t< T_y, T_inv_scale >	stan::math::exponential_cdf (const T_y &y, const T_inv_scale &beta)
	Calculates the exponential cumulative distribution function for the given y and beta.
template<typename T_y , typename T_inv_scale >
return_type_t< T_y, T_inv_scale >	stan::math::exponential_cdf_log (const T_y &y, const T_inv_scale &beta)
template<bool propto, typename T_y , typename T_inv_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_inv_scale > * = nullptr>
return_type_t< T_y, T_inv_scale >	stan::math::exponential_lpdf (const T_y &y, const T_inv_scale &beta)
	The log of an exponential density for y with the specified inverse scale parameter.
template<typename T_inv , class RNG >
VectorBuilder< true, double, T_inv >::type	stan::math::exponential_rng (const T_inv &beta, RNG &rng)
	Return a exponential random variate with inverse scale beta using the specified random number generator.
template<typename T_y , typename T_shape , typename T_scale >
return_type_t< T_y, T_shape, T_scale >	stan::math::frechet_ccdf_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< T_y, T_shape, T_scale >	stan::math::frechet_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
template<typename T_shape , typename T_scale , class RNG >
VectorBuilder< true, double, T_shape, T_scale >::type	stan::math::frechet_rng (const T_shape &alpha, const T_scale &sigma, RNG &rng)
	Return a pseudorandom Frechet variate for the given shape and scale parameters using the specified random number generator.
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type_t< T_y, T_shape, T_inv_scale >	stan::math::gamma_ccdf_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< T_y, T_shape, T_inv_scale >	stan::math::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.
template<typename T_y , typename T_shape , typename T_inv_scale >
return_type_t< T_y, T_shape, T_inv_scale >	stan::math::gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_inv_scale &beta)
template<bool propto, typename T_y , typename T_shape , typename T_inv_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_shape, T_inv_scale > * = nullptr>
return_type_t< T_y, T_shape, T_inv_scale >	stan::math::gamma_lpdf (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.
template<typename T_shape , typename T_inv , class RNG >
VectorBuilder< true, double, T_shape, T_inv >::type	stan::math::gamma_rng (const T_shape &alpha, const T_inv &beta, RNG &rng)
	Return a gamma random variate for the given shape and inverse scale parameters using the specified random number generator.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::gumbel_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &beta)
template<typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::gumbel_cdf (const T_y &y, const T_loc &mu, const T_scale &beta)
	Returns the Gumbel distribution cumulative distribution for the given location and scale.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::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 , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::gumbel_lccdf (const T_y &y, const T_loc &mu, const T_scale &beta)
	Returns the Gumbel log complementary cumulative distribution for the given location and scale.
template<typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::gumbel_lcdf (const T_y &y, const T_loc &mu, const T_scale &beta)
	Returns the Gumbel log cumulative distribution for the given location and scale.
template<bool propto, typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::gumbel_lpdf (const T_y &y, const T_loc &mu, const T_scale &beta)
	Returns the Gumbel log probability density for the given location and scale.
template<typename T_loc , typename T_scale , class RNG >
VectorBuilder< true, double, T_loc, T_scale >::type	stan::math::gumbel_rng (const T_loc &mu, const T_scale &beta, RNG &rng)
	Return a Gumbel random variate with the given location and scale using the specified random number generator.
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::inv_chi_square_ccdf_log (const T_y &y, const T_dof &nu)
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::inv_chi_square_cdf (const T_y &y, const T_dof &nu)
	Returns the inverse chi square cumulative distribution function for the given variate and degrees of freedom.
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::inv_chi_square_cdf_log (const T_y &y, const T_dof &nu)
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::inv_chi_square_lccdf (const T_y &y, const T_dof &nu)
	Returns the inverse chi square log complementary cumulative distribution function for the given variate and degrees of freedom.
template<typename T_y , typename T_dof >
return_type_t< T_y, T_dof >	stan::math::inv_chi_square_lcdf (const T_y &y, const T_dof &nu)
	Returns the inverse chi square log cumulative distribution function for the given variate and degrees of freedom.
template<bool propto, typename T_y , typename T_dof , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_dof > * = nullptr>
return_type_t< T_y, T_dof >	stan::math::inv_chi_square_lpdf (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.
template<typename T_deg , class RNG >
VectorBuilder< true, double, T_deg >::type	stan::math::inv_chi_square_rng (const T_deg &nu, RNG &rng)
	Return a pseudorandom inverse chi squared variate with the nu degrees of freedom using the specified random number generator.
template<typename T_y , typename T_shape , typename T_scale >
return_type_t< T_y, T_shape, T_scale >	stan::math::inv_gamma_ccdf_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< T_y, T_shape, T_scale >	stan::math::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.
template<typename T_y , typename T_shape , typename T_scale >
return_type_t< T_y, T_shape, T_scale >	stan::math::inv_gamma_cdf_log (const T_y &y, const T_shape &alpha, const T_scale &beta)
template<bool propto, typename T_y , typename T_shape , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_shape, T_scale > * = nullptr>
return_type_t< T_y, T_shape, T_scale >	stan::math::inv_gamma_lpdf (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.
template<typename T_shape , typename T_scale , class RNG >
VectorBuilder< true, double, T_shape, T_scale >::type	stan::math::inv_gamma_rng (const T_shape &alpha, const T_scale &beta, RNG &rng)
	Return a pseudorandom inverse gamma variate for the given shape and scale parameters using the specified random number generator.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::logistic_ccdf_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< T_y, T_loc, T_scale >	stan::math::logistic_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
template<typename T_loc , typename T_scale , class RNG >
VectorBuilder< true, double, T_loc, T_scale >::type	stan::math::logistic_rng (const T_loc &mu, const T_scale &sigma, RNG &rng)
	Return a Logistic random variate for the given location and scale using the specified random number generator.
template<typename T_y , typename T_scale , typename T_shape , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_scale, T_shape > * = nullptr>
return_type_t< T_y, T_scale, T_shape >	stan::math::loglogistic_cdf (const T_y &y, const T_scale &alpha, const T_shape &beta)
	The loglogistic cumulative distribution function for the specified scalar(s) given the specified scales(s) and shape(s).
template<bool propto, typename T_y , typename T_scale , typename T_shape , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_scale, T_shape > * = nullptr>
return_type_t< T_y, T_scale, T_shape >	stan::math::loglogistic_lpdf (const T_y &y, const T_scale &alpha, const T_shape &beta)
	The log of the loglogistic density for the specified scalar(s) given the specified scales(s) and shape(s).
template<typename T_scale , typename T_shape , class RNG >
VectorBuilder< true, double, T_scale, T_shape >::type	stan::math::loglogistic_rng (const T_scale &alpha, const T_shape &beta, RNG &rng)
	Return a loglogistic random variate for the given scale and shape parameters using the specified random number generator.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::lognormal_ccdf_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< T_y, T_loc, T_scale >	stan::math::lognormal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
template<typename T_loc , typename T_scale , class RNG >
VectorBuilder< true, double, T_loc, T_scale >::type	stan::math::lognormal_rng (const T_loc &mu, const T_scale &sigma, RNG &rng)
	Return a lognormal random variate for the given location and scale using the specified random number generator.
template<typename T_n , typename T_location , typename T_precision >
return_type_t< T_location, T_precision >	stan::math::neg_binomial_2_ccdf_log (const T_n &n, const T_location &mu, const T_precision &phi)
template<typename T_n , typename T_location , typename T_precision >
return_type_t< T_location, T_precision >	stan::math::neg_binomial_2_cdf_log (const T_n &n, const T_location &mu, const T_precision &phi)
template<typename T_loc , typename T_inv , class RNG >
VectorBuilder< true, int, T_loc, T_inv >::type	stan::math::neg_binomial_2_log_rng (const T_loc &eta, const T_inv &phi, RNG &rng)
	Return a negative binomial random variate with the specified log-location and inverse dispersion parameters using the given random number generator.
template<typename T_loc , typename T_prec , class RNG >
VectorBuilder< true, int, T_loc, T_prec >::type	stan::math::neg_binomial_2_rng (const T_loc &mu, const T_prec &phi, RNG &rng)
	Return a negative binomial random variate with the specified location and precision parameters using the given random number generator.
template<typename T_n , typename T_shape , typename T_inv_scale >
return_type_t< T_shape, T_inv_scale >	stan::math::neg_binomial_ccdf_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< T_shape, T_inv_scale >	stan::math::neg_binomial_cdf_log (const T_n &n, const T_shape &alpha, const T_inv_scale &beta)
template<typename T_shape , typename T_inv , class RNG >
VectorBuilder< true, int, T_shape, T_inv >::type	stan::math::neg_binomial_rng (const T_shape &alpha, const T_inv &beta, RNG &rng)
	Return a negative binomial random variate with the specified shape and inverse scale parameters using the given random number generator.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::normal_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
template<typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::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.
template<typename T_y , typename T_loc , typename T_scale >
return_type_t< T_y, T_loc, T_scale >	stan::math::normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma)
template<bool propto, typename T_y , typename T_loc , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_loc, T_scale >	stan::math::normal_lpdf (T_y &&y, T_loc &&mu, T_scale &&sigma)
	The log of the normal density for the specified scalar(s) given the specified mean(s) and deviation(s).
template<typename T_loc , typename T_scale , class RNG >
VectorBuilder< true, double, T_loc, T_scale >::type	stan::math::normal_rng (const T_loc &mu, const T_scale &sigma, RNG &rng)
	Return a Normal random variate for the given location and scale using the specified random number generator.
template<bool propto, typename T_y , typename T_s , typename T_n , typename T_loc , typename T_scale >
return_type_t< T_y, T_s, T_loc, T_scale >	stan::math::normal_sufficient_lpdf (const T_y &y_bar, const T_s &s_squared, const T_n &n_obs, 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).
template<typename T_y , typename T_scale , typename T_shape >
return_type_t< T_y, T_scale, T_shape >	stan::math::pareto_ccdf_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< T_y, T_scale, T_shape >	stan::math::pareto_cdf_log (const T_y &y, const T_scale &y_min, const T_shape &alpha)
template<typename T_shape , typename T_scale , class RNG >
VectorBuilder< true, double, T_shape, T_scale >::type	stan::math::pareto_rng (const T_scale &y_min, const T_shape &alpha, RNG &rng)
	Return a Pareto random variate for the given shape and scale parameters using the specified random number generator.
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::pareto_type_2_ccdf_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< T_y, T_loc, T_scale, T_shape >	stan::math::pareto_type_2_cdf_log (const T_y &y, const T_loc &mu, const T_scale &lambda, const T_shape &alpha)
template<typename T_loc , typename T_scale , typename T_shape , class RNG >
VectorBuilder< true, double, T_loc, T_scale, T_shape >::type	stan::math::pareto_type_2_rng (const T_loc &mu, const T_scale &lambda, const T_shape &alpha, RNG &rng)
	Return a Pareto type 2 random variate for the given location, scale, and shape using the specified random number generator.
template<typename T_y , typename T_theta >
return_type_t< T_theta >	stan::math::poisson_binomial_ccdf_log (const T_y &y, const T_theta &theta)
template<bool propto, typename T_y , typename T_theta >
return_type_t< T_theta >	stan::math::poisson_binomial_cdf (const T_y &y, const T_theta &theta)
	Returns the CDF for the Poisson-binomial distribution evaluated at the specified number of successes and probabilities of successes.
template<typename T_y , typename T_theta >
return_type_t< T_theta >	stan::math::poisson_binomial_cdf_log (const T_y &y, const T_theta &theta)
template<bool propto, typename T_y , typename T_theta >
return_type_t< T_theta >	stan::math::poisson_binomial_lccdf (const T_y &y, const T_theta &theta)
	Returns the log CCDF for the Poisson-binomial distribution evaluated at the specified number of successes and probabilities of successes.
template<bool propto, typename T_y , typename T_theta >
return_type_t< T_theta >	stan::math::poisson_binomial_lcdf (const T_y &y, const T_theta &theta)
	Returns the log CDF for the Poisson-binomial distribution evaluated at the specified number of successes and probabilities of successes.
template<bool propto, typename T_y , typename T_theta >
return_type_t< T_theta >	stan::math::poisson_binomial_lpmf (const T_y &y, const T_theta &theta)
	Returns the log PMF for the Poisson-binomial distribution evaluated at an specified array of numbers of successes and probabilities of successes.
template<typename T_theta , typename RNG , require_eigen_vt< std::is_arithmetic, T_theta > * = nullptr>
int	stan::math::poisson_binomial_rng (const T_theta &theta, RNG &rng)
	Return a pseudorandom Poisson binomial random variable for the given vector of success parameters using the specified random number generator.
template<typename T_n , typename T_rate >
return_type_t< T_rate >	stan::math::poisson_ccdf_log (const T_n &n, const T_rate &lambda)
template<typename T_n , typename T_rate >
return_type_t< T_rate >	stan::math::poisson_cdf_log (const T_n &n, const T_rate &lambda)
template<typename T_rate , class RNG >
VectorBuilder< true, int, T_rate >::type	stan::math::poisson_log_rng (const T_rate &alpha, RNG &rng)
	Return a Poisson random variate with specified log rate parameter using the given random number generator.
template<typename T_rate , class RNG >
VectorBuilder< true, int, T_rate >::type	stan::math::poisson_rng (const T_rate &lambda, RNG &rng)
	Return a Poisson random variate with specified rate parameter using the given random number generator.
template<typename T_y , typename T_scale >
return_type_t< T_y, T_scale >	stan::math::rayleigh_ccdf_log (const T_y &y, const T_scale &sigma)
template<typename T_y , typename T_scale >
return_type_t< T_y, T_scale >	stan::math::rayleigh_cdf_log (const T_y &y, const T_scale &sigma)
template<typename T_scale , class RNG >
VectorBuilder< true, double, T_scale >::type	stan::math::rayleigh_rng (const T_scale &sigma, RNG &rng)
	Return a Rayleigh random variate with scale parameter sigma using the specified random number generator.
template<typename T_y , typename T_dof , typename T_scale >
return_type_t< T_y, T_dof, T_scale >	stan::math::scaled_inv_chi_square_ccdf_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< T_y, T_dof, T_scale >	stan::math::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.
template<typename T_y , typename T_dof , typename T_scale >
return_type_t< T_y, T_dof, T_scale >	stan::math::scaled_inv_chi_square_cdf_log (const T_y &y, const T_dof &nu, const T_scale &s)
template<bool propto, typename T_y , typename T_dof , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_dof, T_scale > * = nullptr>
return_type_t< T_y, T_dof, T_scale >	stan::math::scaled_inv_chi_square_lpdf (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.
template<typename T_deg , typename T_scale , class RNG >
VectorBuilder< true, double, T_deg, T_scale >::type	stan::math::scaled_inv_chi_square_rng (const T_deg &nu, const T_scale &s, RNG &rng)
	Return a scaled chi square random variate for the given number of degrees of freedom and scale using the specified random number generator.
template<typename T_y , typename T_loc , typename T_scale , typename T_skewness >
return_type_t< T_y, T_loc, T_scale, T_skewness >	stan::math::skew_double_exponential_ccdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_skewness &tau)
template<typename T_y , typename T_loc , typename T_scale , typename T_skewness , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale, T_skewness > * = nullptr>
return_type_t< T_y, T_loc, T_scale, T_skewness >	stan::math::skew_double_exponential_cdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_skewness &tau)
	Returns the skew double exponential cumulative density function.
template<typename T_y , typename T_loc , typename T_scale , typename T_skewness >
return_type_t< T_y, T_loc, T_scale, T_skewness >	stan::math::skew_double_exponential_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_skewness &tau)
template<typename T_y , typename T_loc , typename T_scale , typename T_skewness , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale, T_skewness > * = nullptr>
return_type_t< T_y, T_loc, T_scale, T_skewness >	stan::math::skew_double_exponential_lccdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_skewness &tau)
	Returns the skew double exponential log complementary cumulative density function.
template<typename T_y , typename T_loc , typename T_scale , typename T_skewness , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale, T_skewness > * = nullptr>
return_type_t< T_y, T_loc, T_scale, T_skewness >	stan::math::skew_double_exponential_lcdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_skewness &tau)
	Returns the skew double exponential log cumulative density function.
template<bool propto, typename T_y , typename T_loc , typename T_scale , typename T_skewness , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_loc, T_scale, T_skewness > * = nullptr>
return_type_t< T_y, T_loc, T_scale, T_skewness >	stan::math::skew_double_exponential_lpdf (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_skewness &tau)
	Returns the skew double exponential log probability density function.
template<typename T_loc , typename T_scale , typename T_skewness , class RNG >
VectorBuilder< true, double, T_loc, T_scale, T_skewness >::type	stan::math::skew_double_exponential_rng (const T_loc &mu, const T_scale &sigma, const T_skewness &tau, RNG &rng)
	Return a skew double exponential random variate with the given location scale and skewness using the specified random number generator.
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::skew_normal_ccdf_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< T_y, T_loc, T_scale, T_shape >	stan::math::skew_normal_cdf_log (const T_y &y, const T_loc &mu, const T_scale &sigma, const T_shape &alpha)
template<typename T_loc , typename T_scale , typename T_shape , class RNG >
VectorBuilder< true, double, T_loc, T_scale, T_shape >::type	stan::math::skew_normal_rng (const T_loc &mu, const T_scale &sigma, const T_shape &alpha, RNG &rng)
	Return a Skew-normal random variate for the given location, scale, and shape using the specified random number generator.
template<typename T_y >
return_type_t< T_y >	stan::math::std_normal_ccdf_log (const T_y &y)
template<typename T_y , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y > * = nullptr>
return_type_t< T_y >	stan::math::std_normal_cdf (const T_y &y)
	Calculates the standard normal cumulative distribution function for the given variate.
template<typename T_y >
return_type_t< T_y >	stan::math::std_normal_cdf_log (const T_y &y)
template<bool propto, typename T_y , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y > * = nullptr>
return_type_t< T_y >	stan::math::std_normal_lpdf (const T_y &y)
	The log of the normal density for the specified scalar(s) given a location of 0 and a scale of 1.
template<class RNG >
double	stan::math::std_normal_rng (RNG &rng)
	Return a standard Normal random variate using the specified random number generator.
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::student_t_ccdf_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< T_y, T_dof, T_loc, T_scale >	stan::math::student_t_cdf_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 , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_dof, T_loc, T_scale > * = nullptr>
return_type_t< T_y, T_dof, T_loc, T_scale >	stan::math::student_t_lpdf (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.
template<typename T_deg , typename T_loc , typename T_scale , class RNG >
VectorBuilder< true, double, T_deg, T_loc, T_scale >::type	stan::math::student_t_rng (const T_deg &nu, const T_loc &mu, const T_scale &sigma, RNG &rng)
	Return a student-t random variate for the given degrees of freedom, location, and scale using the specified random number generator.
template<typename T_y , typename T_low , typename T_high >
return_type_t< T_y, T_low, T_high >	stan::math::uniform_ccdf_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< T_y, T_low, T_high >	stan::math::uniform_cdf_log (const T_y &y, const T_low &alpha, const T_high &beta)
template<bool propto, typename T_y , typename T_low , typename T_high , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_low, T_high > * = nullptr>
return_type_t< T_y, T_low, T_high >	stan::math::uniform_lpdf (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.
template<typename T_alpha , typename T_beta , class RNG >
VectorBuilder< true, double, T_alpha, T_beta >::type	stan::math::uniform_rng (const T_alpha &alpha, const T_beta &beta, RNG &rng)
	Return a uniform random variate for the given upper and lower bounds using the specified random number generator.
template<typename T_x , typename T_mu , typename T_k >
return_type_t< T_x, T_mu, T_k >	stan::math::von_mises_ccdf_log (const T_x &x, const T_mu &mu, const T_k &k)
template<typename T_x , typename T_mu , typename T_k >
return_type_t< T_x, T_mu, T_k >	stan::math::von_mises_cdf (const T_x &x, const T_mu &mu, const T_k &k)
	Calculates the cumulative distribution function of the von Mises distribution:
template<typename T_x , typename T_mu , typename T_k >
return_type_t< T_x, T_mu, T_k >	stan::math::von_mises_cdf_log (const T_x &x, const T_mu &mu, const T_k &k)
template<typename T_x , typename T_mu , typename T_k >
return_type_t< T_x, T_mu, T_k >	stan::math::von_mises_lccdf (const T_x &x, const T_mu &mu, const T_k &k)
	Calculates the log of the complement of the cumulative distribution function of the von Mises distribution:
template<typename T_x , typename T_mu , typename T_k >
return_type_t< T_x, T_mu, T_k >	stan::math::von_mises_lcdf (const T_x &x, const T_mu &mu, const T_k &k)
	Calculates the log of the cumulative distribution function of the von Mises distribution:
template<typename T_loc , typename T_conc , class RNG >
VectorBuilder< true, double, T_loc, T_conc >::type	stan::math::von_mises_rng (const T_loc &mu, const T_conc &kappa, RNG &rng)
	Return a von Mises random variate for the given location and concentration using the specified random number generator.
template<typename T_y , typename T_shape , typename T_scale >
return_type_t< T_y, T_shape, T_scale >	stan::math::weibull_ccdf_log (const T_y &y, const T_shape &alpha, const T_scale &sigma)
template<typename T_y , typename T_shape , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_shape, T_scale > * = nullptr>
return_type_t< T_y, T_shape, T_scale >	stan::math::weibull_cdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
	Returns the Weibull cumulative distribution function for the given location and scale.
template<typename T_y , typename T_shape , typename T_scale >
return_type_t< T_y, T_shape, T_scale >	stan::math::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 , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_shape, T_scale > * = nullptr>
return_type_t< T_y, T_shape, T_scale >	stan::math::weibull_lccdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
	Returns the Weibull log complementary cumulative distribution function for the given location and scale.
template<typename T_y , typename T_shape , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_shape, T_scale > * = nullptr>
return_type_t< T_y, T_shape, T_scale >	stan::math::weibull_lcdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
	Returns the Weibull log cumulative distribution function for the given location and scale.
template<bool propto, typename T_y , typename T_shape , typename T_scale , require_all_not_nonscalar_prim_or_rev_kernel_expression_t< T_y, T_shape, T_scale > * = nullptr>
return_type_t< T_y, T_shape, T_scale >	stan::math::weibull_lpdf (const T_y &y, const T_shape &alpha, const T_scale &sigma)
	Returns the Weibull log probability density for the given location and scale.
template<typename T_shape , typename T_scale , class RNG >
VectorBuilder< true, double, T_shape, T_scale >::type	stan::math::weibull_rng (const T_shape &alpha, const T_scale &sigma, RNG &rng)
	Return a Weibull random variate for the given shape and scale parameters using the specified random number generator.
template<bool propto = false, typename T_y , typename T_a , typename T_t0 , typename T_w , typename T_v , typename T_sv , typename T_sw , typename T_st0 >
auto	stan::math::wiener_lpdf (const T_y &y, const T_a &a, const T_t0 &t0, const T_w &w, const T_v &v, const T_sv &sv, const T_sw &sw, const T_st0 &st0, const double &precision_derivatives=1e-4)
	The log of the first passage time density function for a (Wiener) drift diffusion model with up to 7 parameters, where $y\in \mathbb{R}_{+}$ is the reacion time, $a \in \mathbb{R}_{+}$ the boundary separation, $t_0 \in \mathbb{R}_{\geq 0}$ the non-decision time, $w \in (0, 1)$ the relative starting point (aka a-priori bias), $v \in \mathbb{R}$ the drifte rate, $s_v \in \mathbb{R}_{\geq 0}$ the inter-trial variability of the drift rate, $s_w \in [0, 1)$ the inter-trial variability of the relative starting point, and $s_{t_0} \in \mathbb{R}_{\geq 0}$ the inter-trial variability of the non-decision time.
template<bool propto, typename T_y , typename T_alpha , typename T_tau , typename T_beta , typename T_delta >
return_type_t< T_y, T_alpha, T_tau, T_beta, T_delta >	stan::math::wiener_lpdf (const T_y &y, const T_alpha &alpha, const T_tau &tau, const T_beta &beta, const T_delta &delta)
	The log of the first passage time density function for a (Wiener) drift diffusion model for the given $y$, boundary separation $\alpha$, nondecision time $\tau$, relative bias $\beta$, and drift rate $\delta$.