Bayesian estimation of the tail index of a heavy tailed distribution under random censoring

Bayesian estimation of the tail index of a heavy-tailed distribution is addressed when data are randomly right-censored. Maximum a posteriori and mean posterior estimators are constructed for various prior distributions of the tail index. Convergence of the posterior distribution of the tail index to a Gaussian distribution is established. Finite-sample properties of the proposed estimators are investigated via simulations. Tail index estimation requires selecting an appropriate threshold for constructing relative excesses. A Monte Carlo procedure is proposed for tackling this issue. Finally, the proposed estimators are illustrated on a medical dataset.