Title: New Weibull-Pareto Poisson distribution: properties, actuarial measures and applications

Authors: Fastel Chipepa; Mavis Pararai; Wilbert Nkomo

Addresses: Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana ' Department of Mathematical Sciences, Faculty of Sciences, Indiana University of Pennsylvania, Pennsylvania, USA ' Department of Mathematics and Statistical Sciences, Faculty of Sciences, Botswana International University of Science and Technology, P. Bag 16, Palapye, Botswana

Abstract: A new power series distribution called the new Weibull-Pareto Poisson distribution is developed. The proposed model is very flexible in modelling heavy-tailed data. Some of the statistical properties are also derived and these include moments, moment generating function, and Rényi entropy. We derive the maximum likelihood estimates of the model parameters. We also derive risk measures, conduct and present their numerical simulations. Numerical simulations results for actuarial risk measures show that the new developed model is heavy-tailed compared to its nested models and some competing models. A Monte Carlo simulation study was also conducted to evaluate the consistency of the model parameter estimates. The results from this study confirm that the developed model produce consistent and reliable parameter estimates. Two heavy-tailed real data examples are used to demonstrate the usefulness of the new proposed model.

Keywords: Weibull-Pareto distribution; power series distribution; maximum likelihood estimation; risk measures; Poisson distribution.

DOI: 10.1504/IJMOR.2025.146353

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.4, pp.415 - 434

Received: 18 Aug 2023
Accepted: 23 Aug 2023
Published online: 27 May 2025 *

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