chi_square_lpdf() [2/3]

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.

The degrees of freedom parameter must be greater than 0. y must be greater than or equal to 0.

\begin{eqnarray*} y &\sim& \chi^2_\nu \\ \log (p (y \, |\, \nu)) &=& \log \left( \frac{2^{-\nu / 2}}{\Gamma (\nu / 2)} y^{\nu / 2 - 1} \exp^{- y / 2} \right) \\ &=& - \frac{\nu}{2} \log(2) - \log (\Gamma (\nu / 2)) + (\frac{\nu}{2} - 1) \log(y) - \frac{y}{2} \\ & & \mathrm{ where } \; y \ge 0 \end{eqnarray*}

Template Parameters

T_y	type of scalar
T_dof	type of degrees of freedom

Parameters

y	A scalar variable.
nu	Degrees of freedom.

Exceptions

std::domain_error	if nu is not greater than or equal to 0
std::domain_error	if y is not greater than or equal to 0.

Definition at line 46 of file chi_square_lpdf.hpp.