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

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.