Author： Alhejaili Amal D. Abd-Elfattah Ehab F.
Publisher： Taylor & Francis Ltd
ISSN： 0361-0926
Source： Communications in Statistics: Theory and Methods, Vol.42, Iss.20, 2013-10, pp. : 3735-3743
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Abstract
One of the common used classes of distributions is the stopped-sum class. This class includes Hermite distribution, Polya–Aeppli distribution, Poisson-Gamma distribution, and Neyman type A. This article introduces the saddlepoint approximations to the stopped-sum class in continuous and discrete settings. We discuss approximations for mass/density and cumulative distribution functions of stopped-sum distributions. Examples of continuous and discrete distributions from the Poisson stopped-sum class are presented. Comparisons between saddlepoint approximations and the exact calculations show the great accuracy of the saddlepoint methods.
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