A.6 Inverse chi distribution

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

if , or equivalently if it has density

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

and it has density

The mean and variance do not greatly simplify. They are

but very good approximations, at least if , are

[see Novick and Jackson (1974, Section 7.3)]. The mode is exactly

and a good approximation to the median at least if is (ibid.)