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 ...
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