Confidence interval estimation of the shape parameter of pareto distribution using extreme order statistics

Abstract

The asymptotic distributions of several estimators of the shape parameter α of the Pareto distribution in the case where the scale parameter is known are derived. The study is carried out using simple random sampling (SRS), extreme ranked set sampling (ERSS) and on random samples that are based on minimum order statistics only or maximum order statistics only. These distributions are used to construct asymptotic confidence intervals (ACI) for α. A simulation study then compares these confidence intervals via their expected lengths and coverage probabilities.