  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.
