An Investigation of Inference of the Generalized Extreme Value Distribution Based on Record

Abstract

In this article, the maximum likelihood and Bayes estimates of the generalized extreme value distribution based on record values are investigated. The asymptotic confidence intervals as well as bootstrap confidence are proposed. The Bayes estimators cannot be obtained in closed form so the MCMC method are used to calculate Bayes estimates as well as the credible intervals. A numerical example is provided to illustrate the proposed estimation methods developed here.

Keywords: Generalized extreme value distribution, Record values, Maximum likelihood estimation, Bayesian estimation.