Ein neuer Ansatz zur Frequenzmodellierung im Versicherungswesen (A new Approach to frequency modeling in risk theory)

Abstract: The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as Binomial-, Negative binomial- or Poisson distributions. Since these distributions sometimes do not really fit to the data we propose a different approach here for claim frequencies via random proportions of the number of insurance contracts. This approach also allows for a statistical goodness-of-fit test via quantile-quantile-plots and can likewise be applied to the modelling of claim size distributions.