inv_chi_square_log() [1/2]

template<bool propto, typename T_y , typename T_dof >

return_type_t< T_y, T_dof > stan::math::inv_chi_square_log	(	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.

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

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

Deprecated:

use inv_chi_square_lpdf

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.

Template Parameters

T_y	Type of scalar.
T_dof	Type of degrees of freedom.

Definition at line 33 of file inv_chi_square_log.hpp.