A light-tail Pareto Type Ⅱ model for disability and reliability case studies with potential risk assessment under disability prevalence dates data in Saudi Arabia

Atef F. Hashem; Mohamed A. Abdelkawy; Haitham M. Yousof; Atef F. Hashem; Mohamed A. Abdelkawy; Haitham M. Yousof

doi:10.3934/math.2025863

AIMS Mathematics

2025, Volume 10, Issue 8: 19300-19334. doi: 10.3934/math.2025863

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A light-tail Pareto Type Ⅱ model for disability and reliability case studies with potential risk assessment under disability prevalence dates data in Saudi Arabia

1.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
2.
King Salman Center for Disability Research, Riyadh 11614, Saudi Arabia
3.
Department of Statistics, Mathematics and Insurance, Benha University, Egypt

Received: 20 June 2025 Revised: 01 August 2025 Accepted: 13 August 2025 Published: 25 August 2025
MSC : 62N05, 62E11, 62H05, 62F10, 62P05, 62G32, 60E05, 62F15

We introduce a new flexible statistical model for disability and reliability case studies, designed to enhance modeling capabilities in reliability engineering and disability prevalence analysis. This model extends the classical Pareto Type Ⅱ distribution by incorporating additional shape parameters, allowing for greater flexibility in modeling various hazard rate shapes and tail behaviors, particularly light tails. Essential properties of the model are explored. The model's applicability and risk assessment potential are demonstrated through case studies: one focusing on reliability engineering (aircraft windshield failure and service times) and another analyzing disability prevalence rates in Saudi Arabia for 2016. Advanced tail analysis tools such as the Hill estimator, Value-at-Risk (VaR), and Peaks Over a Random Threshold (PORT) were employed. The analyses reveal that the proposed OGPTII model offers superior goodness-of-fit compared to several existing models for both reliability and Saudi Arabia disability data, accurately captures the light-tailed nature of the datasets, and provides crucial insights into potential risk factors. This makes it a valuable tool for predictive maintenance strategies in engineering and for evidence-based policy planning and resource allocation in the context of disability management.
Citation: Atef F. Hashem, Mohamed A. Abdelkawy, Haitham M. Yousof. A light-tail Pareto Type Ⅱ model for disability and reliability case studies with potential risk assessment under disability prevalence dates data in Saudi Arabia[J]. AIMS Mathematics, 2025, 10(8): 19300-19334. doi: 10.3934/math.2025863

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Abstract

We introduce a new flexible statistical model for disability and reliability case studies, designed to enhance modeling capabilities in reliability engineering and disability prevalence analysis. This model extends the classical Pareto Type Ⅱ distribution by incorporating additional shape parameters, allowing for greater flexibility in modeling various hazard rate shapes and tail behaviors, particularly light tails. Essential properties of the model are explored. The model's applicability and risk assessment potential are demonstrated through case studies: one focusing on reliability engineering (aircraft windshield failure and service times) and another analyzing disability prevalence rates in Saudi Arabia for 2016. Advanced tail analysis tools such as the Hill estimator, Value-at-Risk (VaR), and Peaks Over a Random Threshold (PORT) were employed. The analyses reveal that the proposed OGPTII model offers superior goodness-of-fit compared to several existing models for both reliability and Saudi Arabia disability data, accurately captures the light-tailed nature of the datasets, and provides crucial insights into potential risk factors. This makes it a valuable tool for predictive maintenance strategies in engineering and for evidence-based policy planning and resource allocation in the context of disability management.

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