${\displaystyle \alpha >{\frac {p-1}{2}}}$ shape parameter (real)
${\displaystyle \beta >0}$ scale parameter

${\displaystyle {\boldsymbol {\Sigma }}}$

${\displaystyle p\times p}$

${\displaystyle {\frac {|{\boldsymbol {\Sigma }}|^{-\alpha }}{\beta ^{p\alpha }\,\Gamma _{p}(\alpha )}}|\mathbf {X} |^{\alpha -{\frac {p+1}{2}}}\exp \left({\rm {tr}}\left(-{\frac {1}{\beta }}{\boldsymbol {\Sigma }}^{-1}\mathbf {X} \right)\right)}$

• ${\displaystyle \Gamma _{p}}$ is the multivariate gamma function.