Forecasting of claim by combining probability distributions

Abstract

Purpose- The purpose of this study is to focus on forecasting the total claim distribution of fire-disaster and transportation insurances by combining probabilities of claim distribution using the data for 2014 and 2015. Methodology- In this study, the combination of Weibull and Gamma distributions of fire-disaster and transport policies are discussed. By combining two different probability density function (PDF), a single PDF is derived and thus it is aimed to provide convenience in calculations. Findings - Two probability distributions were combined with mathematical methods. As a result, a single probability density function was obtained. This probability density function can represent the total claim distribution. Conclusion- In conclusion, we used the data regarding fire-disaster and transportation insurances for 2014 and 2015. Insurance firms that offer these two policies to their customers need to determine their risk taking into consideration the total claim distribution from the policies. Since Weibull and Gamma distributions have a PDF, it is necessary to integrate the multiplication of the characteristic functions for combining these two distributions. The PDF obtained as a result of mathematical operations is the PDF of the total claim distribution.