Modeling third-party liability insurance claims: An exponential mixture distribution and parametric bootstrap-based solution - Ainani Tajriyan Muntaharridwan; Aceng Komarudin Mutaqin (Desimal: Jurnal Matematika, 2025)
This study aims to model large third-party liability insurance claim data using an exponential mixture distribution with a parametric bootstrap approach. The research seeks to identify a suitable exponential mixture distribution and determine its properties, such as the mean, standard deviation, and probability. The methodology involves modeling the large third-party liability insurance claim data using an exponential mixture distribution where the mixing distribution is determined through a parametric bootstrap approach. The parametric bootstrap is utilized to generate a mixing distribution, with inverse gamma and inverse exponential distributions considered as candidates. The selection of the mixing distribution is based on the p-value of the Kolmogorov-Smirnov test and the log-likelihood function value. The parameters of the chosen exponential mixture distribution are estimated using the maximum likelihood method via the Newton-Raphson iteration. The data used is from a comprehensive third-party liability extension for category 2 vehicles in DKI Jakarta, Jawa Barat, and Banten for the 2018 underwriting year. The results of the analysis indicate that the exponential-inverse gamma mixture distribution is suitable for modeling the large claim data. The estimated mean value is IDR 4,318,360, the estimated standard deviation is IDR 6,797,485, and the estimated probability is 0.6950.