A general insurance risk model consists of in initial reserve, the premiums
collected, the return on investment of these premiums, the claims frequency
and the claims sizes. Except for the initial reserve, these components are
all stochastic. The assumption of the distributions of the claims sizes is an
integral part of the model and can greatly in
uence decisions on reinsurance
agreements and ruin probabilities.
An array of parametric distributions are available for use in describing the
distribution of claims. The study is focussed on parametric distributions
that have positive skewness and are de ned for positive real values. The
main properties and parameterizations are studied for a number of distributions.
Maximum likelihood estimation and method-of-moments estimation
are considered as techniques for tting these distributions. Multivariate numerical
maximum likelihood estimation algorithms are proposed together
with discussions on the e ciency of each of the estimation algorithms based
on simulation exercises. These discussions are accompanied with programs
developed in SAS PROC IML that can be used to simulate from the various
parametric distributions and to t these parametric distributions to
The presence of heavy upper tails in the context of general insurance claims
size distributions indicates that there exists a high risk of observing very
large and even extreme claims. This needs to be allowed for in the modeling
of claims. Methods used to describe tail weight together with techniques
that can be used to detect the presence of heavy upper tails are studied.
These methods are then applied to the parametric distributions to classify
their tails' heaviness.
The study is concluded with an application of the techniques developed
to t the parametric distributions and to evaluate the tail heaviness of reallife
claims data. The goodness-of- t of the various tted distributions are
discussed. Based on the nal results further research topics are identi ed.