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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 42, Fasc. 1,
pages 63 - 80
DOI: 10.37190/0208-4147.00056
Published online 20.6.2022
 

Poisson approximation to the convolution of power series distributions

A. N. Kumar
P. Vellaisamy

Abstract: In this article, we obtain, for the total variation distance, error bounds for Poisson approximation to the convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several Poisson limit theorems follow as corollaries from our bounds. As applications, we compare Poisson approximation results with negative binomial approximation results for sums of Bernoulli, geometric, and logarithmic series random variables.

2010 AMS Mathematics Subject Classification: Primary 62E17; Secondary 62E20, 60F05, 60E05.

Keywords and phrases: convolution of distributions, Poisson and negative binomial approximation, power series distribution, Stein's method.

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