A New Version of the Compound Quasi-Lomax Model: Properties, Characterizations and Risk Analysis under the U.K. Motor Insurance Claims Data

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Detalles Bibliográficos
Publicado en:	Pakistan Journal of Statistics and Operation Research vol. 21, no. 3 (2025), p. 341-363
Autor principal:	Hashim, Mujtaba
Otros Autores:	Butt, Nadeem S, Hamedani, G G, Ibrahim, Mohamed, Al-Nefaie, Abdullah H, AboAlkhair, Ahmad M, Yousof, Haitham M
Publicado:	University of the Punjab, College of Statistical & Actuarial Science
Materias:	Maximum likelihood estimation Risk management Performance evaluation Insurance claims Insurance Risk analysis Root-mean-square errors Extreme values Risk assessment Survival analysis Parameter estimation Insurance industry
Acceso en línea:	Citation/Abstract Full Text - PDF
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Descripción
Resumen:	This paper introduces a new lifetime distribution, the Compound Quasi-Lomax (CQLx) model, designed to enhance the modeling of heavy-tailed data in actuarial and financial risk analysis. The CQLx distribution is developed through a novel extension of the Lomax family, offering increased flexibility in capturing extreme values and complex data behaviors. Key mathematical properties are derived. Characterization of the model is achieved via truncated moments and the reverse hazard function. Several estimation methods are employed including the Maximum Likelihood Estimation (MLE), Cramér-von Mises (СУМ), Anderson-Darling Estimation (ADE), Right-Tail Anderson-Darling Estimation (RTADE), and Left-Tail Anderson-Darling Estimation (LTADE). A comprehensive simulation study evaluates the performance of these methods in terms of bias and root mean square error (RMSE) across various sample sizes. Risk measures such as Value-at-Risk (VaR), Tail Value-at-Risk (TVaR), Tail Variance (TV), Tail Mean Variance (TMV), and Expected Loss (EL) are computed under artificial and real financial insurance claims data. The results demonstrate that MLE generally provides the most accurate and stable estimates, particularly for larger samples, while CVM and ADE tend to overestimate risk, especially at higher quantiles. The CQLx model shows superior performance in fitting extreme claim-size data, making it a robust tool for risk management.
ISSN:	1816-2711 2220-5810
DOI:	10.18187/pjsor.v21i3.4494
Fuente:	Advanced Technologies & Aerospace Database