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- Publisher
- Taylor & Francis
- Copyright
- Copyright Taylor & Francis Group, LLC
- ISSN
- 1532-4141
- eISSN
- 0361-0918
- DOI
- 10.1080/03610919808813465
- Publisher site
- See Article on Publisher Site
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.
Journal
Communications in Statistics: Simulation and Computation – Taylor & Francis
Published: Jan 1, 1998
Keywords: Mixed Poisson distribution; inverted gamma; weighted distribution; Taylor expansion; limiting case; asymptotic behaviour