On Maximum Likelihood Estimates for the Shape Parameter of the Generalized Pareto Distribution

Abstract

The general Pareto distribution (GPD) has been widely used a lot in the extreme value for example to model exceedance over a threshold. Feature of The GPD that when applied to real data sets depends substantially and clearly on the parameter estimation process. Mostly the estimation is preferred by maximum likelihood because have a consistent estimator with lowest bias and variance. The objective of the present study is to develop efficient estimation methods for the maximum likelihood estimator for the shape parameter or extreme value index. Which based on the numerical methods for maximizing the log-likelihood by introduce an algorithm for computing maximum likelihood estimate of The GPD parameters. Finally, a numerical examples are given to illustrate the obtained results, they are carried out to investigate the behavior of the method.

Keywords: Extreme Value Index, Generalized Pareto Distributions, Excesses Over High Thresholds, Maximum Likelihood, The Modified Bisection Method Algorithm

JEL Classification: B26, C13, C15, C24, C58 ,G22, G32