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A Novel Generated G Family for Risk Analysis and Assessment under Different Non-Bayesian Methods: Properties, Characterizations and Applications to USA House Prices and UK Insurance Claims Data

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Publicado en:Pakistan Journal of Statistics and Operation Research vol. 21, no. 4 (2025), p. 507-530
Autor principal: Ibrahim, Mohamed
Otros Autores: Al-Nefaie, Abdullah H, Butt, Nadeem S, Hamedani, G G, Hashim, Mujtaba, Aboalkhair, Ahmad M, Ahmed, Nazar Ali, Roushdy, Noura, Yousof, Haitham M, Nabawy, Noha
Publicado:
University of the Punjab, College of Statistical & Actuarial Science
Materias:
Probability density functions
Maximum likelihood estimation
Parameterization
Risk assessment
Parameter estimation
Bayesian analysis
Insurance claims
Insurance
Risk analysis
Distribution functions
Acceso en línea:Citation/Abstract
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Resumen:This study proposes a new and versatile family of continuous probability models known as the log-exponential generated (LEG) distributions, with particular emphasis on the log-exponential generated Weibull (LEGW) model as its prominent representative. By introducing an additional layer of parameterization, the family offers improved adaptability in shaping distributional forms, especially regarding skewness and heavy-tailed behavior. The LEGW formulation proves especially relevant for reliability data and for capturing rare but impactful events where asymmetry plays a major role. The work details the theoretical framework of the family through explicit expressions for its cumulative distribution function (CDF) and probability density function (PDF), alongside the corresponding hazard rate function (HRF). Several analytical characteristics are also investigated, including series representations and behavior in the extreme tail. To demonstrate practical value, the paper conducts risk evaluations employing sophisticated key risk indicators (KRIs) such as Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), and tail meanvariance measure (TMVq) across multiple quantile levels. Parameter estimation is addressed using several techniques, including maximum likelihood estimation (MLE), the Cramér-von Mises approach (CVM), and the Anderson-Darling estimator (ADE), in addition to their right-tail adjusted (RTADE) and left-tail adjusted variants (LTADE) to better capture extreme behaviors. Comparative performance analyses are carried out using both controlled simulation scenarios and real data from the insurance and housing sectors to test robustness under heavytail conditions. The findings highlight the effectiveness of the LEGW model in applied risk assessment, supported by evidence from insurance claims and economic datasets.
ISSN:1816-2711
2220-5810
DOI:10.18187/pjsor.v21i4.4797
Fuente:Advanced Technologies & Aerospace Database