Modified bisection algorithm in estimating the extreme value index under random censoring

Abstract

The Generalized Pareto Distribution (GPD) has long been employed in the theories of extreme values. In this paper, we are interested by estimating the extreme value index under censoring. Using a maximum likelihood estimator (MLE) and a numerical method algorithm, a new approach is proposed to estimate the extreme value index by maximizing the adaptive log-likelihood of GPD given censored data. We also show how to construct the maximum likelihood estimate of the GPD parameters (shape and scale) using censored data. Lastly, numerical examples are provided at the end of the paper to show the method’s reliability and to better illustrate the findings of this research.