Statistical Analysis of Stable Distribution Application in Non Life İnsurance

Abstract

In recent years, the theory of stable variables has seen many exciting developments, due to the fact that it is a very rich class of probability laws able to represent different asymmetries, and heavy tails, so modelling complex phenomena; unlike normal law, which very often underestimates extreme events. α-stable distributions are a class of heavy-tailed distributions. For that, we will start in this paper by presenting a review of graphical tests, which will help us to verify if we are in the presence of data with infinite variance or not, and more precisely of stable distribution. Then we will apply these tests to real data representing car claim amounts, allowing us to assume that our sample follows a stable distribution. In order to confirm this hypothesis, we will therefore estimate the four parameters of the distribution using the McCuloch method, as well as the Koutrouvelis method in order to be able to make the diagnosis with Kernel Densities, and finally we will demonstrate that α-stable distribution is better fitted to the car claim amount data by using the Kolmogorov test.

Keywords

• stable distribution
• infinite variance
• simulation
• statistical test