Modeling Vehicle Insurance Loss Data Using a New Member of T-X Family of Distributions

Abstract

In actuarial literature, we come across a diverse range of probability distributions for fitting insurance loss data. Popular distributions are lognormal, log-t, various versions of Pareto, log-logistic, Weibull, gamma and its variants and a generalized beta of the second kind, among others. In this paper, we try to supplement the distribution theory literature by incorporating the heavy tailed model, called weighted T-X Weibull distribution. The proposed distribution exhibits desirable properties relevant to the actuarial science and inference. Shapes of the density function and key distributional properties of the weighted T-X Weibull distribution are presented. Some actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are calculated. A simulation study based on the actuarial measures is provided. Finally, the proposed method is illustrated via analyzing vehicle insurance loss data.

Keywords

• Heavy-tailed distributions
• Weibull distribution
• Insurance losses
• Actuarial measures
• Monte Carlo simulation
• Estimation