A New G Family: Properties, Characterizations, Different Estimation Methods and PORT-VaR Analysis for U.K. Insurance Claims and U.S. House Prices Data Sets

Authors

Ahmad M. AboAlkhair, King Faisal University
Gholamhossein Hamedani, Marquette UniversityFollow
Nazar Ali Ahmed, King Faisal University
Mohamed Ibrahim, King Faisal University
Mohammad A. Zayed, Imam Mohammad Ibn Saud Islamic University
Haitham M. Yousof, Benha University

Document Type

Article

Publication Date

2025

Publisher

MDPI

Source Publication

Mathematics

Source ISSN

2227-7390

Abstract

This paper introduces a new class of probability distributions, termed the generated log exponentiated polynomial (GLEP) family, designed to enhance flexibility in modeling complex real financial data. The proposed family is constructed through a novel cumulative distribution function that combines logarithmic and exponentiated polynomial structures, allowing for rich distributional shapes and tail behaviors. We present comprehensive mathematical properties, including useful series expansions for the density, cumulative, and quantile functions, which facilitate the derivation of moments, generating functions, and order statistics. Characterization results based on the reverse hazard function and conditional expectations are established. The model parameters are estimated using various frequentist methods, including Maximum Likelihood Estimation (MLE), Cramer–von Mises (CVM), Anderson–Darling (ADE), Right Tail Anderson–Darling (RTADE), and Left Tail Anderson–Darling (LEADE), with a comparative simulation study assessing their performance. Risk analysis is conducted using actuarial key risk indicators (KRIs) such as Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), Tail Variance (TV), Tail Mean Variance (TMV), and excess function (EL), demonstrating the model’s applicability in financial and insurance contexts. The practical utility of the GLEP family is illustrated through applications to real and simulated datasets, including house price dynamics and insurance claim sizes. Peaks Over Random Threshold Value-at-Risk (PORT-VaR) analysis is applied to U.K. motor insurance claims and U.S. house prices datasets. Some recommendations are provided. Finally, a comparative study is presented to prove the superiority of the new family.

Comments

Published version. Mathematics, Vol. 13, No. 19 (2025) : DOI. © 2025 MDPI. Used with permission.

Recommended Citation

AboAlkhair, Ahmad M.; Hamedani, Gholamhossein; Ahmed, Nazar Ali; Ibrahim, Mohamed; Zayed, Mohammad A.; and Yousof, Haitham M., "A New G Family: Properties, Characterizations, Different Estimation Methods and PORT-VaR Analysis for U.K. Insurance Claims and U.S. House Prices Data Sets" (2025). Mathematical and Statistical Science Faculty Research and Publications. 151.
https://epublications.marquette.edu/math_fac/151