exponential_lpdf() [1/3]

template<bool propto, typename T_y_cl , typename T_inv_scale_cl , require_all_prim_or_rev_kernel_expression_t< T_y_cl, T_inv_scale_cl > * = nullptr, require_any_not_stan_scalar_t< T_y_cl, T_inv_scale_cl > * = nullptr>

return_type_t< T_y_cl, T_inv_scale_cl > stan::math::exponential_lpdf ( const T_y_cl &  y, const T_inv_scale_cl &  beta  )

inline

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*}

Template Parameters

T_y_cl	type of scalar
T_inv_scale_cl	type of inverse scale

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.

Definition at line 47 of file exponential_lpdf.hpp.