uniform_lpdf() [2/3]

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.

\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*}

Template Parameters

T_y	type of scalar
T_low	type of lower bound
T_high	type of upper bound

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

Definition at line 47 of file uniform_lpdf.hpp.