Estimation of the generalized Pareto distribution

This paper provides precise arguments to explain the anomalous behavior of the likelihood surface when sampling from the generalized Pareto distribution for small or moderate samples. The behavior of the profile-likelihood function is characterized in terms of the empirical coefficient of variation. A sufficient condition is given for the global maximum of the likelihood function of the Pareto distribution to be at a finite point. (C) 2008 Elsevier B.V. Ail rights reserved.