Estimating a Common Parameter of Two Farlie-Gumbel-Morgenstern Bivariate Uniform Distributions by Induced Ranked Set Sampling

Ranked set sampling from several populations

Abstract

The method of ranked set sampling when units are to be induced from several bivariate populations is introduced in this work. The best linear unbiased estimator (BLUE) of the common parameter θ₂, based on n ranked set observations, is obtained when n₁ observations are drawn from one of the two Farlie-Gumbel-Morgenstern (FGM) bivariate uniform distributions and n₂ observations, drawn from the other FGM bivariate uniform distribution such that n = n₁ + n₂. The BLUE of θ₂ based on the upper extreme ranked set sample is also obtained. These estimators are compared with the usual BLUE of the common parameter θ₂ based on the concomitants of order statistics of an equivalent sample size.