Work

Regression Extensions of the New Polynomial Exponential Distribution: NPED-GLM and Poisson–NPED Count Models with Applications in Engineering and Insurance

Year: 2026

Type: article

Abstract: The New Polynomial Exponential Distribution (NPED), introduced by Beghriche et al. (2022), provides a flexible one-parameter family capable of representing diverse hazard shapes and heavy-tailed behavior. Regression frameworks based on the NPED, however, have not yet been established. This paper introduces two methodological extensions: (i) a generalized linear model (NPED-GLM) in which the distribution parameter depends on covariates, and (ii) a Poisson–NPED count regression model suitable for overdispersed and heavy-tailed count data. Likelihood-based inference, asymptotic properties, and simulation studies are developed to investigate the performance of the estimators. Applications to engineering failure-count data and insurance claim frequencies illustrate the advantages of the proposed models relative to classical Poisson, negative binomial, and Poisson–Lindley regressions. These developments substantially broaden the applicability of the NPED in actuarial science, reliability engineering, and applied statistics.

Source: Computation

DOI: 10.3390/computation14010026

Authors: Halim Zeghdoudi, Sandra S. Ferreira, Vinoth Raman, Dário Ferreira

Institutions: Badji Mokhtar-Annaba University, University of Beira Interior, Imam Abdulrahman Bin Faisal University

Language: English

Topic: Statistical Distribution Estimation and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,172

Funder: Fundação para a Ciência e a Tecnologia