A flexible accelerated Weibull distribution for actuarial risk analysis: Theoretical and empirical evaluation with real claims data

Mohamed Ibrahim; Hafida Goual; Khaoula Kaouter Meribout; Ahmad M. AboAlkhair; Gadir Alomair; Haitham M. Yousof; Mohamed Ibrahim; Hafida Goual; Khaoula Kaouter Meribout; Ahmad M. AboAlkhair; Gadir Alomair; Haitham M. Yousof

doi:10.3934/math.2025796

AIMS Mathematics

2025, Volume 10, Issue 8: 17868-17893. doi: 10.3934/math.2025796

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A flexible accelerated Weibull distribution for actuarial risk analysis: Theoretical and empirical evaluation with real claims data

1.
Department of Quantitative Methods, School of Business, King Faisal University, Al Ahsa 31982, Saudi Arabia
2.
Laboratory of probabilities and statistics LaPS, Badji Mokhtar-Annaba University, 12, P.O. Box 23000, Annaba, Algeria
3.
Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt

Received: 21 June 2025 Revised: 17 July 2025 Accepted: 24 July 2025 Published: 07 August 2025
MSC : 60E05, 62G05, 62N05, 62P30

This paper proposed a novel accelerated failure time (AFT) model based on the weighted Topp-Leone Weibull (WTLW) distribution, designed for robust survival analysis under censored and uncensored actuarial and biomedical data. The AFT-WTLW model introduced flexible hazard rate shapes, validated through goodness-of-fit tests and real applications, including electric insulating fluid failure times and body fat percentage datasets. Parameter estimation employed maximum likelihood (MLE), Cramér -von Mises (CVM), Anderson-Darling (ADE), right tail Anderson-Darling (RTADE) and left tail Anderson-Darling (LTADE), with simulation studies demonstrating RTADE's superior accuracy in bias and root mean squared error (RMSE) for small-to-moderate samples. The model's risk assessment capabilities were highlighted via value-at-risk (VaR), tail VaR (TVaR), and tail mean-variance metrics, revealing RTADE and ADE as optimal for capturing extreme tail risks. A modified Nikulin-Rao-Robson (NRR) chi-square test confirmed the AFT-WTLW's validity for censored data, with empirical rejection levels aligning closely with theoretical thresholds. Applications to motor failure data and Johnson's body fat dataset illustrated its practical utility in actuarial, healthcare, and engineering domains. Computational efficiency was achieved via the Barzilai–Borwein optimization (BBO) algorithm for parameter optimization. Simulation results emphasized improved estimation consistency with increasing sample sizes, particularly for RTADE in high-quantile risk metrics.
- accelerated failure time,
- censored data,
- risk analysis,
- goodness-of-fit tests,
- value-at-risk,
- Barzilai-Borwein optimization,
- biomedical data,
- reliability engineering
Citation: Mohamed Ibrahim, Hafida Goual, Khaoula Kaouter Meribout, Ahmad M. AboAlkhair, Gadir Alomair, Haitham M. Yousof. A flexible accelerated Weibull distribution for actuarial risk analysis: Theoretical and empirical evaluation with real claims data[J]. AIMS Mathematics, 2025, 10(8): 17868-17893. doi: 10.3934/math.2025796

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Abstract

This paper proposed a novel accelerated failure time (AFT) model based on the weighted Topp-Leone Weibull (WTLW) distribution, designed for robust survival analysis under censored and uncensored actuarial and biomedical data. The AFT-WTLW model introduced flexible hazard rate shapes, validated through goodness-of-fit tests and real applications, including electric insulating fluid failure times and body fat percentage datasets. Parameter estimation employed maximum likelihood (MLE), Cramér -von Mises (CVM), Anderson-Darling (ADE), right tail Anderson-Darling (RTADE) and left tail Anderson-Darling (LTADE), with simulation studies demonstrating RTADE's superior accuracy in bias and root mean squared error (RMSE) for small-to-moderate samples. The model's risk assessment capabilities were highlighted via value-at-risk (VaR), tail VaR (TVaR), and tail mean-variance metrics, revealing RTADE and ADE as optimal for capturing extreme tail risks. A modified Nikulin-Rao-Robson (NRR) chi-square test confirmed the AFT-WTLW's validity for censored data, with empirical rejection levels aligning closely with theoretical thresholds. Applications to motor failure data and Johnson's body fat dataset illustrated its practical utility in actuarial, healthcare, and engineering domains. Computational efficiency was achieved via the Barzilai–Borwein optimization (BBO) algorithm for parameter optimization. Simulation results emphasized improved estimation consistency with increasing sample sizes, particularly for RTADE in high-quantile risk metrics.

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