In classical credibility theory we assume that the vector of claims conditionally on has independent components with identical means. However, this assumption is sometimes unrealistic. To relax this condition Hachemeister (Hachemeister, C.A., 1975. Credibility for regression models with...

In the present paper we develop more efficient recursive formulae for the evaluation of the t-order cumulative function [Gamma]th(x) and the t-order tail probability [Lambda]th(x) of the class of compound Poisson distributions in the case where the derivative of the probability generating...

In this paper, we develop links between credibility theory and quantiles. More specifically, we show how quantiles can be embedded within the classical Bühlmann’s (1967) credibility model and within Hachemeister’s (1975) regression credibility model. The context of influence function is...

Empirical credibility estimation, which is a credibility counterpart of empirical Bayes estimation, lacks robustness due to the sensitivity of estimators to outlier events. In this paper we combine robust statistics with empirical linear Bayes estimation and derive robust asymptotic optimality...