Estimation of the location and scale parameters of a power-function distribution by linear functions of order statistics

Abstract

Suppose are the order statistics of a random sample of size n from the power-function distribution with distribution function . Using linear combinations of the order statistics , best linear unbiased estimators of (1) α when β and y are known, (2) γ when α and γ are known, (3) α and β when γ is known, are derived.