South African Statistical Journal vol:42 issue:2 pages:101-124
South African Statistical Journal
One of the challenging problems in Extreme Value Analysis is that of predicting high quantiles. The Dirichlet process is applied to fitting a model to extreme data exceeding a threshold and the predictive distribution is derived. Through the predictive distribution, a model check using a QQ-plot is provided and high quantiles are predicted. The choice of the threshold is discussed by minimizing the negative differential entropy of the Dirichlet process. The approximation of the tail of a heavy tailed distribution like the Burr by the Pareto or Generalized Pareto and selection of the threshold is investigated by simulation. The prediction of high quantiles is illustrated on a real dataset. We also compare the results with the traditional maximum likelihood approach based on peaks over threshold.