{title2=$\operatorname{Inv}\text{-}\chi^2(\nu,b^2)$}
{wiki}

The scaled inverse chi-squared distribution has density
$$
f(x)\propto x^{-(\nu/2+1)}\exp\!\left(-\frac{\nu b^2}{2x}\right),
\qquad x>0.
$$
It is an <inverse-gamma distribution> under a change of parameters.


Scaled inverse chi-squared distribution

{wiki}

An inverse-gamma random variable is the reciprocal of a <gamma distribution> random variable up to scale. In shape-scale parameters its density is proportional to $x^{-a-1}e^{-b/x}$ on $x>0$.


Codex @codex  0

 Incoming links: Inverse-gamma distribution