Shrinkage Estimators Of Scale Parameter Towards An Interval Of Morgenstern Type Bivariate Uniform Distribution Using Ranked Set Sampling

Abstract

Ranked set sampling (RSS) is a method of sampling that can be advantageous when quantification of all sampling units is costly but a small set of units can be easily ranked, according to the charac ter under investigation, without actual quantification. The technique was first introduced by McIntyre (1952) for estimating mean pasture and forage yields. The theory and applications of RSS are given by Chen et al. (2004). Suppose the variable of interest, Y, is difficult or much too expen sive to measure, but an auxiliary variable X correlated with Y is readily measureable and can be ordered exactly. In this case, as an alternative to McIntyre’s (1952) method of ranked set sampling, Stokes (1977) used an auxiliary variable for the ranking of sampling units. If XðrÞr is the observation measured on the auxiliary variable X from the unit chosen from the rth set then we write Y½r r to denote the corresponding measurement made on the study variable Y on this unit, then Y½r r;r 5 1; 2; ...; n, from the ranked set sample. Clearly, Y½r r is the concomitant of the rth order sta tistic arising from the rth sample. Stokes (1995) has obtained the estimation of parameters of the location-scale family of distribution by RSS. Lam et al. (1994) used RSS to estimate the two parameter exponential distribution. Al-Saleh and Ananbeh (2005, 2007) estimated the means of the bivariate normal distribution using moving extremes RSS with a concomitant variable. Al-Saleh and Diab (2009) considered estimation of the parameters of Downton’s bivariate exponential distri bution using an RSS scheme. Barnett and Moore (1997) derived the best linear unbiased estimator (BLUE) for the mean of Y, based on a ranked set sample obtained using an auxiliary variable X for ranking the sample units