exponential_lpdf() [2/3]

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.

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	type of scalar
T_inv_scale	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 52 of file exponential_lpdf.hpp.