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

Author

Listed:
  • 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
    Department of Mathematics, Faculty of Science, Tanta University, Tanta 31111, Egypt)

  • Aminh M. Alnaghmosh

    (Department of Mathematics and Statistics, College of Science, King Faisal University, Alahsa 31982, Saudi Arabia)

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.

Suggested Citation

  • Fatimah E. Almuhayfith & Sudeep R. Bapat & Hassan S. Bakouch & Aminh M. Alnaghmosh, 2023. "A Flexible Semi-Poisson Distribution with Applications to Insurance Claims and Biological Data," Mathematics, MDPI, vol. 11(5), pages 1-15, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1122-:d:1078397
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    References listed on IDEAS

    as
    1. Mullahy, John, 1986. "Specification and testing of some modified count data models," Journal of Econometrics, Elsevier, vol. 33(3), pages 341-365, December.
    2. Gómez-Déniz, Emilio & Sarabia, José María & Calderín-Ojeda, Enrique, 2011. "A new discrete distribution with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 406-412, May.
    3. D. Böhning & E. Dietz & P. Schlattmann & L. Mendonça & U. Kirchner, 1999. "The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(2), pages 195-209.
    4. William H. Greene, 1994. "Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models," Working Papers 94-10, New York University, Leonard N. Stern School of Business, Department of Economics.
    5. Deepesh Bhati & Hassan S. Bakouch, 2019. "A new infinitely divisible discrete distribution with applications to count data modeling," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(6), pages 1401-1416, March.
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