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Published:
Feb 25, 2025Keywords:
Rare event; convolution method; Poisson distribution; Skewness; Kurtosis
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Sum of Poisson-Distributed Random Variables: A Convolution Method Approach
Abstract
This paper presents a two-parameter extension of the classical Poisson distribution, specifically tailored for rare event modeling. The proposed model is constructed as the sum of two independent Poisson random variables, using a convolution method. Some properties of the distribution, including the probability mass function (PMF), moment-generating function (MGF), mean, variance, higher-order moments, Skewness, and kurtosis, are derived.
