Testy dobré shody pro Paretovo rozdělení

Abstract

Pareto model is widely used in insurance and reinsurance, as well as in finance (capital management, stock returns), and in modelling of natural disasters. As a motivation, we introduce a case study drawn from the pricing of reinsurance excess of loss contracts. In the first chapter of the thesis, we define four types of Pareto distributions and explore such properties as moments, parameter estimation and characterizations. In the follow- ing chapter, we examine the theory of unbiased estimation in order to better understand the construction of goodness-of-fit tests based on characterizations. Subsequently, we introduce an overview of some goodness-of-fit tests. The final chapter focuses on simu- lating the type I error rates and power of these tests, as well as conducting a comparative analysis. Finally, we return to the motivational example and complete the calculation of the price for the reinsurance coverage. 1