A short comment on the paper “A simple method to estimate parametric claim size distributions from grouped data”, by Brix, J. and Pfeifer, D.

Conclusion

We conclude that fitting a GPD over the threshold value u=20000 and estimating its parameters by means of thex ²-method is not as poor as claimed in Brix and Pfeifer [1]. It seems that the EVT based approach provides even better estimates than the method proposed in [1] when modeling extreme tail events, see the values n₁ and the corresponding values KI_NEW for u₁≥ 100000 onwards. We also believe that there is no major drawback when using estimation techniques which incorporate the cummulative distribution function rather than the density function. In case the cumulative distribution functions should not be implemented in a (statistical) software package, one can easily get around this problem by applying standard numerical integration techniques.