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

Fatimah E. Almuhayfith (), Sudeep R. Bapat, Hassan S. Bakouch and Aminh M. Alnaghmosh
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Fatimah E. Almuhayfith: Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia
Sudeep R. Bapat: Department of Operations Management and Quantitative Techniques, Indian Institute of Management, Indore 453556, India
Hassan S. Bakouch: Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Aminh M. Alnaghmosh: Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia

Mathematics, 2023, vol. 11, issue 5, 1-15

Abstract: 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: discrete distributions; over-dispersion; recurrence relation for the moments; entropy; estimation; simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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