On the Maximum Likelihood Estimation for the Transmuted Extreme Value Distribution Parameters

Abstract

Recently, researchers have been interested in the transmuted family of distributions via the quadratic rank transformation map, which was studied by Shaw and Buckley [21] (2009). Among the important distributions is the generalized extreme value distribution, due to its wide use in various fields. For this reason, we focus on estimating the parameters of the transmuted generalized extreme value (TGEV) distribution. Therefore, we develop transformed parameters of a generalized Pareto distribution (GPD) with a scale parameter and a shape parameter and approximate it to the transformed conditional distribution function to estimate the parameters of the TGEV via the maximum likelihood estimation (MLE). In a ddition, we present a numerical method for estimating the unknown parameters of the transmuted GPD starting from the MLE based on simple random sampling (SRS) and ranked set sampling (RSS). Finally, we present a simulation study using this practical method to better illustrate the findings of this investigation.

Keywords: Generalized Pareto distributions; Excesses over high thresholds; Maximum Likelihood Estimation; Ranked set sampling; Modified Bisection Algorithm.

2010 Mathematics Subject Classification. 62G32; 60G70