Modelling extreme claims using generalised pareto distributions family in an insurance company

Abstract

The project focuses on modeling and estimating loss claims from Insurance company. Generalized Pareto distributions family was used and compared to come with a best fitting distribution. These distributions include Exponential, Pareto and Uniform distribution. In the methodology the project shows how to develop the distributions from one distribution. Three methods for estimating parameters of the distributions were used i.e .the maximum likelihood method, the method of moments and L moment method. Properties of each distribution were shown. Then measures of risk were derived. In application, Using the three methods of estimations to come up with the best fitting distribution. I’ll also compare the three methods of estimations and come up with the best method. In addition .Using the best two distributions I’ll plot histogram and QQ plot to come up with the best distribution. Thereafter I will estimate the confidence intervals of the chosen distribution parameter estimate using the bootstrap method.