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In this paper, a recent novel approach is applied to estimate the threshold parameter of a composite model. Several composite models from Transformed Gamma and Inverse Transformed Gamma families are constructed based on this approach and their parameters are estimated by the maximum likelihood method. These composite models are fitted to allocated loss adjustment expenses (ALAE). In comparison to all composite models studied, the composite Weibull-Inverse Transformed Gamma model is proved to be a competitor candidate as it best fit the loss data. The final part considers the backtesting method to verify the validation of VaR and CTE risk measures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]