摘要：Based on the fact that any heavy tailed distribution can be approxi-
mated by a possibly in nite mixture of Pareto distributions, this paper proposes
two Bayesian methodologies tailored to infer on distribution tails belonging to the
Frechet domain of attraction. Firstly, a Bayesian Pareto based clustering pro-
cedure is developed, where the mixing distribution is chosen to be the classical
conjugate prior of the Pareto distribution. This allows the grouping of n objects
into a certain number of clusters according to their extremal behavior and also
exhibits a new estimator for the tail index. Secondly, a nonparametric extension
of the model based clustering is proposed in which the parameter of interest is
the mixing distribution. Estimation of the tail probability is conducted using a
Dirichlet process prior for the unknown mixing distribution. To illustrate, both
methodologies are applied to simulated data sets and a real data set concerning
dietary exposure to a mycotoxin called Ochratoxin A.
关键词：Dirichlet process, Model Based clustering, Ochratoxin A, Tail index
estimation.
