Order statistics from the Burr type X model

Abstract

The Burr type X distribution function studied here, F( x; θ) = (1 − e − x 2 ) θ , has shape parameter θ > 0 and is defined for all real x ≥ 0. In this paper, the exact form of the probability density function and moments of the r th-order statistic in a sample of size n from F are derived. Measures of skewness and kurtosis of the pdf for different choices of r, n, and θ are presented. Two types of estimators of location and scale parameters based on some observed order statistics have also been discussed.