Abstract
The generalized Pareto (GP) distribution is the most popular model for extreme values. Recently, Papastathopoulos and Tawn [Journal of Statistical Planning and Inference 143 (2013), 131-143] have proposed some generalizations of the GP distribution for improved modeling. Here, we point that Papastathopoulos and Tawn’s generalizations are in fact not new and then go on to propose a tractable generalization of the GP distribution. For the latter generalization, we provide a comprehensive treatment of mathematical properties, estimate parameters by the method of maximum likelihood and provide the observed information matrix. The proposed model is shown to give a better fit for the real data set used in Papastathopoulos and Tawn.