For estimating the shape parameter of Paretian excess claims, certain Bayesian estimators, which are closely related to the Hill estimator, have been suggested in the insurance literature. It turns out that these estimators may have a poor performance – just as the Hill estimator – if a certain location parameter is unequal to zero in the Paretian modeling. In an alternative formulation this means that a scale parameter is unequal to 1. Thus, it suggests itself to add the scale parameter in the modeling and to deal with Bayesian estimators of the shape and scale parameters in a full Paretian model. These estimators will be applied to fire and motor reinsurance data. The performance of these estimators will be illustrated by means of Monte Carlo simulations.
