Inverse matrix gamma distribution

Notation ${\displaystyle {\rm {IMG}}_{p}(\alpha ,\beta ,{\boldsymbol {\Psi }})}$ ${\displaystyle \alpha }$ shape parameter (real) ${\displaystyle \beta >0}$ scale parameter ${\displaystyle {\boldsymbol {\Psi }}}$ scale (positive-definite real ${\displaystyle p\times p}$ matrix) ${\displaystyle \mathbf {X} }$ positive-definite real ${\displaystyle p\times p}$ matrix ${\displaystyle {\frac {|{\boldsymbol {\Psi }}|^{\alpha }}{\beta ^{p\alpha }\Gamma _{p}(\alpha )}}|\mathbf {X} |^{-\alpha -(p+1)/2}\exp \left({\rm {tr}}\left(-{\frac {1}{\beta }}{\boldsymbol {\Psi }}\mathbf {X} ^{-1}\right)\right)}$ ${\displaystyle \Gamma _{p}}$ is the multivariate gamma function.
This reduces to the inverse Wishart distribution with ${\displaystyle \nu }$ degrees of freedom when ${\displaystyle \beta =2,\alpha ={\frac {\nu }{2}}}$.