Truncated gamma-truncated Weibull distribution for modeling claim severity

Abstract

Modeling the data with a standard distribution is usually difficult to do because of the different characteristics of the body and tail in data. For example, Gamma distribution that has the right-skewing and light tail characteristics is considered unable to model the amount of claim that has a heavy tail. However, the correct fit of the model in the body data and tail data is important in analyzing the risk. Therefore, the splicing distribution is introduced at a threshold value that separates the body and the tail of data. In this paper, splicing distribution at a threshold value is used to model the amount of claim that has heavy tails. The splicing distribution in this paper links a light-tailed distribution for the body data and heavy-tailed distribution for the tail data. In this paper, the splicing distribution of the Truncated Gamma is used to model the data of Phoenix City claim below the threshold value and the Truncated Weibull distribution to model the data above the threshold value. By considering the result of the Kolmogorov-Smirnov test, it can be concluded that this distribution is suitable for modeling Phoenix City claim dataset.