A New Weighted Lindley Model with Applications to Extreme Historical Insurance Claims

Morad Alizadeh, Mahmoud Afshari, Gauss M. Cordeiro, Ziaurrahman Ramaki, Javier E. Contreras-Reyes (), Fatemeh Dirnik and Haitham M. Yousof
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Morad Alizadeh: Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, Iran
Mahmoud Afshari: Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, Iran
Gauss M. Cordeiro: Department of Statistics, Federal University of Pernambuco, Recife 50670-901, Brazil
Ziaurrahman Ramaki: Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, Iran
Javier E. Contreras-Reyes: Instituto de Matemática, Física y Estadística, Facultad de Ingeniería y Negocios, Universidad de Las Américas, Sede Viña del Mar, 7 Norte 1348, Viña del Mar 2531098, Chile
Fatemeh Dirnik: Department of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, Iran
Haitham M. Yousof: Department of Statistics, Mathematics and Insurance, Benha University, Benha 13518, Egypt

Stats, 2025, vol. 8, issue 1, 1-20

Abstract: In this paper, we propose a weighted Lindley (NWLi) model for the analysis of extreme historical insurance claims. It extends the classical Lindley distribution by incorporating a weight parameter, enabling more flexibility in modeling insurance claim severity. We provide a comprehensive theoretical overview of the new model and explore two practical applications. First, we investigate the mean-of-order P (MOOP ( P ) ) approach for quantifying the expected claim severity based on the NWLi model. Second, we implement a peaks over a random threshold (PORT) analysis using the value-at-risk metric to assess extreme claim occurrences under the new model. Further, we provide a simulation study to evaluate the accuracy of the estimators under various methods. The proposed model and its applications provide a versatile tool for actuaries and risk analysts to analyze and predict extreme insurance claim severity, offering insights into risk management and decision-making within the insurance industry.

Keywords: extreme claim; Lindley model; mean-of-order P; peaks over a random threshold; value-at-risk; weighted models (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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