Bayesian Statistics: An Introduction, 4th Edition

A.18 Behrens’ distribution

X is said to have Behrens’ (or Behrens–Fisher or Fisher–Behrens) distribution with degrees of freedom and and angle , denoted

if X has the same distribution as

where T1 and T2 are independent and

Equivalently, X has density

where

over the whole real line, where

This distribution naturally arises as the posterior distribution of

when we have samples of size from ...