چکیده
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: 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.
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