2024/12/12 by Chudamani Poudyal, Poudyal, Chudamani, Gokarna Aryal +3
Mathematics · Computer Science · #Advanced Statistical Methods and Models #Statistical Distribution Estimation and Applications #Bayesian Methods and Mixture Models
paper · pdf · doi:10.48550/arxiv.2412.09830
Statistical modeling of claim severity distributions is essential in\ninsurance and risk management, where achieving a balance between robustness and\nefficiency in parameter estimation is critical against model contaminations.\nTwo ( L )-estimators, the method of trimmed moments (MTM) and the method of\nwinsorized moments (MWM), are commonly used in the literature, but they are\nconstrained by rigid weighting schemes that either discard or uniformly\ndown-weight extreme observations, limiting their customized adaptability. This\npaper proposes a flexible robust ( L )-estimation framework weighted by\nKumaraswamy densities, offering smoothly varying observation-specific weights\nthat preserve valuable information while improving robustness and efficiency.\nThe framework is developed for parametric claim severity models, including\nPareto, lognormal, and Fr 'echet distributions, with theoretical\njustifications on asymptotic normality and variance-covariance structures.\nThrough simulations and application to a U.S. indemnity loss dataset, the\nproposed method demonstrates superior performance over MTM, MWM, and MLE\napproaches, particularly in handling outliers and heavy-tailed distributions,\nmaking it a flexible and reliable alternative for loss severity modeling.\n