Likelihood moment estimation for the generalized pareto distribution

Traditional methods for estimating parameters in the generalized Pareto distribution have theoretical and computational defects. The moment estimator and the probability-weighted moment estimator have low asymptotic efficiencies. They may not exist or may give nonsensical estimates. The maximum likelihood estimator, which sometimes does not exist, is asymptotically efficient, but its computation is complex and has convergence problems. The likelihood moment estimator is proposed, which is computationally easy and has high asymptotic efficiency.