Composite Weibull-Inverse Transformed Gamma distribution and its actuarial application

Abstract

This paper introduces a new composite model, namely, composite Weibull-Inverse Transformed Gamma distribution which assumes Weibull distribution for the head up to a specified threshold and inverse transformed gamma distribution beyond it. The closed form of probability density function (pdf) as well as the estimation of parameters by maximum likelihood method is presented. The model is compared with several benchmark distributions and their performances are measured. A well-known data set, Danish fire loss data, is used for this purpose and it's Value at Risk (VaR) using the new model is computed. In comparison to several standard models, the composite Weibull- Inverse Transformed Gamma model proved to be a competitor candidate.