Saddlepoint Approximations for Stopped-Sum Distributions |
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Authors: | Amal D Alhejaili Ehab F Abd-Elfattah |
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Institution: | 1. Deanship of Educational Services , Taibah University , Madinah , Kingdom of Saudi Arabia amolah1429@hotmail.com;3. Department of Mathematics, Faculty of Education , Ain Shams University , Cairo , Egypt |
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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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Keywords: | Poisson-Gamma stopped-sum Polya–Aeppli stopped-sum distribution Saddlepoint approximations stopped-sum distribution |
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