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

Ahmad M. AboAlkhair, G. G. Hamedani, Nazar Ali Ahmed, Mohamed Ibrahim (), Mohammad A. Zayed and Haitham M. Yousof
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Ahmad M. AboAlkhair: Department of Quantitative Methods, School of Business, King Faisal University, Al Ahsa 31982, Saudi Arabia
G. G. Hamedani: Department of Mathematical and Statistical Sciences, Marquette University, Marquette, WI 53233, USA
Nazar Ali Ahmed: Department of Quantitative Methods, School of Business, King Faisal University, Al Ahsa 31982, Saudi Arabia
Mohamed Ibrahim: Department of Quantitative Methods, School of Business, King Faisal University, Al Ahsa 31982, Saudi Arabia
Mohammad A. Zayed: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
Haitham M. Yousof: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13511, Egypt

Mathematics, 2025, vol. 13, issue 19, 1-35

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.

Keywords: house prices data; Value-at-Risk; Weibull model; claims data; risk analysis; characterizations; Peaks Over Random Threshold Value-at-Risk (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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