  The upper tail of a claim size distribution of a property line of business is
frequently modelled by Pareto distribution. However, the upper tail does not
need to be Pareto distributed, extraordinary shapes are possible. Here, the
opportunities for the modelling of loss distributions are extended. The basic
idea is the adjustment of a base distribution for their tails. The
(generalised) Pareto distribution is used as base distribution for different
reasons. The upper tail is in the focus and can be modelled well for special
cases by a discrete mixture of the base distribution with a combination of the
base distribution with an adapting distribution via the product of their
survival functions. A kind of smoothed step is realised in this way in the
original line function between logarithmic loss and logarithmic exceedance
probability. The lower tail can also be adjusted. The new approaches offer the
opportunity for stochastic interpretation and are applied to observed losses.
For parameter estimation, a modification of the minimum Anderson Darling
distance method is used. A new test is suggested to exclude that the observed
upper tail is better modelled by a simple Pareto distribution. Q-Q plots are
applied, and secondary results are also discussed.

Methodology