Abstract
In this paper we consider a two parameter ratio-product-ratio estimator for estimating population mean in case of post stratification following the estimator due to Chami et al (2012). The bias and mean squared error of proposed estimator are obtained to the first degree of approximation. We derive conditions under which the proposed estimator has smaller mean squared error than the sample mean , ratio estimator and product estimators . Empirical studies gives insight on the magnitude of the efficiency of the estimator developed.
Highlights
The post stratification was first introduced by Holt and Smith (1979) and Ige and Tripathi (1989)
It is known that when the auxiliary information is used at the estimation stage, the ratio estimator is best among a wide class of estimators when the relation between y and x, the variate under study and auxiliary variate, respectively is a straight line through the origin and the variance of y about this line is proportional to x
The regression line does not pass well as that of regression estimator. Keeping this fact in view and due to the stronger intuitive appeal, statisticians are more inclined towards the use of the ratio and the product estimators and a large amount of work has been carried out towards the modification of ratio and product estimators, for instance, see Singh (1986), Singh and Espejo (2003) etc
Summary
The principal aim of statistical surveys is to obtain information about of interest. To increase the precision of the estimates we use information on the auxiliary variable. Chouhan (2012) proposed class of ratio type estimators using various known parameters of auxiliary variates in case of post stratification. Keeping in this view we have suggested. Where x ps = Wh xh is the unbiased estimate of population means in case of post stratification, X = Wh X h is h=1 h=1 the known population mean of the auxiliary variate x and xh is the mean of the sample of size nh that fall in the hth stratum. Motivated by Khoshnevisan et al (2007), we define a class of separate ratio-type estimators for population mean Y in post stratified sampling as ( ) ( ) Lps ah X h + bh gh YSR = h=1 wh yh h ah xh + bh + (1− h ) ah X h + bh ,. Numerical examples are given in support of the present study
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