Abstract
The Poisson–inverse Gaussian distribution is expressed in terms of a mixed Poisson distribution with the inverted gamma as mixing distribution. A simple approximation by Taylor expansion is derived for the Poisson–inverse Gaussian probabilities from this mixing expression. Based on this expansion, the asymptotic behaviour is considered. Shaban's approximation (Communications in Statistics, A, 1981, pp. 1389–1399) of the Poisson-inverse Gaussian probability by its limiting case is examined, and it is shown that this approximation can be improved by using the inverted gamma mixing formulation.
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