A.5 Inverse chi-squared distribution

X has an inverse chi-squared distribution on ν degrees of freedom, denoted

if , or equivalently if it has density

If , so that , then Y is S times an inverse chi-squared distribution on ν degrees of freedom, denoted

and it has density

The mean and variance are

The mode is

and the median is in the range

provided , with the upper limit approached closely when [see Novick and Jackson (1974, Section 7.5)].