ON THE EFFICIENCY OF A DUAL TO RATIO-CUM-PRODUCT ESTIMATOR IN SAMPLE SURVEYS

Abstract

AbstractThis article suggests a dual to ratio-cum-product estimator for flnite populationmean that is complementary, in a certain sense, to the commonly used ratio-cum-product estimator reported by Singh [4]. The expressions for bias and meansquare error of the proposed estimator have been obtained to the flrst degree ofapproximation. This study also generalises the work of Srivenkataramana [5] andBandyopadhyay [1]. To illustrate the results an empirical study is carried out.1. IntroductionLet U be a flnite population consisting of N units u 1 ;u 2 ;:::;u N . The units of thisflnite population are identiflable in the sense that they are uniquely labelled from1 to N and the label of each unit is known. Let y and ( x;z ) denote the studyvariate and auxiliary variates taking the values y i and ( x i ;z i ), respectively, on theunit u i ( i = 1 ; 2 ;:::;N ), where x is positively correlated with y and z is negativelycorrelated with y . We wish to estimate the population mean Y„ = (1 =N )P Ni =1