Distributions of Generalized Order Statistics and Parameters Estimation of Pareto Distribution in Statistical Explicit Forms

Abstract

Abstract : We study some distributions of generalized order statistics (GOS) for Pareto distribution. In particular, we have derived the joint probability density function (pdf) for GOS from Pareto distribution in statistical explicit form. In addition, the joint pdf of both range and midrange for GOS from Pareto distribution is obtained. The estimation of Pareto distribution parameters based on GOS using the method of Maximum Likelihood Estimators (MLE) have been derived in explicit forms. Furthermore, some special cases have been discussed. Keywords Pareto Distribution, Generalized Order Statistics, Ordinary Order Statistics, Maximum Likelihood Estimation.