Mathematics (Feb 2023)

A Flexible Semi-Poisson Distribution with Applications to Insurance Claims and Biological Data

  • Fatimah E. Almuhayfith,
  • Sudeep R. Bapat,
  • Hassan S. Bakouch,
  • Aminh M. Alnaghmosh

DOI
https://doi.org/10.3390/math11051122
Journal volume & issue
Vol. 11, no. 5
p. 1122

Abstract

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In this paper, a discrete one-parameter distribution called the semi-Poisson distribution is introduced, which is based on a set of non-negative integers. It is seen that this distribution captures over-dispersion and zero-inflation scenarios well. A few properties of the proposed distribution, such as moments, the probability-generating function, index of dispersion, recurrence relation for the moments, and negative moments are presented. The distribution is applied to two real-life datasets related to insurance claims and parasite counts, where it is noted to perform better than many of the existing discrete distributions based on Z+, including some of the recently introduced ones.

Keywords