The Empirical Bayes Estimation of Risk Parameters in Pareto Claim Distribution

The Bayesian model is established in this paper, and the risk parameters of claim amounts in Pareto distribution are estimated. The maximum likelihood estimation, Bayesian estimation and credibility estimation are derived and the strong consistency of these estimates are proved. We also compared their mean square error both in theory and in numerical simulation. The results show that Bayesian estimation is better than other estimates in sense of mean square error. Finally, the structural parameters in Bayes estimation and credibility estimation are estimated and the corresponding empirical Bayes estimates are proved asymptotically optimal.