Parametrizace rozdělení škod v neživotním pojištení

Title: Parameterization of claims distribution in non-life insurance Author: Bc. Mária Špaková Department: Department of Probability and Mathematical Statistics Supervisor: RNDr. Michal Pešta Ph.D., MFF UK Abstract: This paper deals with the parameterization of claim size distributions in non-life insurance. It consists of the theoretical and the practical part. In the first part we discuss the usual distributions of claims and their properties. One section is devoted to extreme values distributions. Consequently, we mention the most known methods for parameter estimation - the maximum likelihood method, the method of moments and the method of weighted moments. The last theoretical chapter is focused on some validation techniques and goodness-of-fit tests. In the practical part we apply some of the discussed approaches on real data. However, we concentrate mainly on the large claims modeling - firstly, we select a reasonable threshold for our data and then we fit the claims by the generalized Pareto distribution together with the introduced parameterization procedures. Based on the results of the applied validation methods we will choose appropriate models for the biggest claims. Keywords: parameterization, non-life insurance, claims distribution