scaled_inv_chi_square_lpdf() [1/3]

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

return_type_t< T_y_cl, T_dof_cl, T_scale_cl > stan::math::scaled_inv_chi_square_lpdf ( const T_y_cl &  y, const T_dof_cl &  nu, const T_scale_cl &  s  )

inline

The log of a scaled inverse chi-squared density for y with the specified degrees of freedom parameter and scale parameter.

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

Template Parameters

T_y_cl	type of random variable
T_dof_cl	type of degrees of freedom
T_Scale_cl	type of scale

Parameters

y	random variable
nu	degrees of freedom
s	Scale parameter.

Exceptions

std::domain_error	if nu is not greater than 0
std::domain_error	if s is not greater than 0.
std::domain_error	if y is not greater than 0.

Definition at line 43 of file scaled_inv_chi_square_lpdf.hpp.