ABSTRACT
The inverse Gaussian density function
g(t) = (=2t
)
1=2
exp
(t )
=2t
(t; ; > 0) (4.1)
arises as the density of the rst passage time of the Brownian motion with
positive drift [153]. The model has been used in reliability theory and in the
theory of demographic rates. Good proposed the generalized inverse Gaussian
distribution
h(t) =
I(; a; b)
t
exp
at bt
t > 0; a > 0; b > 0
; (4.2)
which was used by Sichel to construct the mixture of Poisson distributions
([123], [153]).
