| Claim Size Distributions |
| Written by theoretic |
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In this section we are interested in the question: What are realistic claim size distributions? This question is about the goodness of fit of the claim size data to the chosen distribution. It is not our goal to give sophisticated statistical analyzes, but we rather aim at introducing some classes of distributions used in insurance practice, which are sufficiently flexible and give a satisfactory fit to the data. In Section 3.2.1 we introduce QQ-plots and in Section 3.2.3 mean excess plots as two graphical methods for discriminating between different claim size distributions. Since realistic claim size distributions are very often heavy-tailed, we start in Section 3.2.2 with an informal discussion of the notions of heavy-and light-tailed distributions. In Section 3.2.4 we introduce some of the major claim size distributions and discuss their properties. In Sections 3.2.5 and 3.2.6 we continue to discuss natural heavy-tailed distributions for insurance: the classes of the distributions with regularly varying tails and the subex-ponential distributions. The latter class is by now considered as the class of distributions for modeling large claims. |