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

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