 Inverse-gamma distribution

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 $x>0$.

The Inverse-Gamma distribution is a continuous probability distribution that is often used in Bayesian statistics, particularly in the context of prior distributions for variances. It is a two-parameter distribution that is defined over positive real numbers.