Empirical model-building and response surface
Empirical model-building and response surface
Statistical inference
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
Numerical Optimization: Theoretical and Practical Aspects (Universitext)
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On of the main problems in financial and actuarial mathematics is to estimate certain loss distributions, to find a distribution that fits best the claims data. As the tail of the loss distribution is especially important, there are two general approaches: to observe the tail behaviour only (or separately) or the whole distribution. In this work we examine the latter. We focus on the problem of fitting a best suitable distribution to Estonian traffic insurance data from 2006 to 2007. The research was initiated by Estonian Traffic Insurance Fund and therefore is of practical importance. The data is quite typical for insurance claims: it contains a lot of observations and is heavy-tailed. In this work we consider five commonly used distributions as possible estimates: Pareto, lognormal, beta, gamma and Weibull. The fitting techniques are based on moment matching or maximum likelihood estimators. For testing goodness of fit (GOF) several classical tests including Chi-square test and Kolmogorov-Smirnov test are used. The accuracy of our approach is evaluated by matching the first and second moments and by plotting PDF-s and CDF-s.