European Journal of Molecular & Clinical Medicine

Abstract

In survey sampling, auxiliary information provided by the auxiliary variables can be used to improve the precision of the estimators. Improved estimators can be developed by using auxiliary information at the estimation stage in order to estimate the population mean.In this paper, modified class of product type estimatorsfor estimation of population mean using auxiliary variable have been proposed. Relative bias andRelative mean square errors of the proposed estimators have been derived upto order O (n-1) and O (n-2) respectively and their efficiencies have been compared with the conventional product estimator and the estimators proposed by Robson (1957), Singh (1989), Dubey (1993) and Sharma et al., (2007).An empirical study has also been carried out through simulationin order to demonstratethe efficiencies of the proposed estimators using two population datasets P1 and P2.The empirical study showed that proposed product type estimator 𝒕(𝟑)∗=𝒚̅𝒑+𝟑𝒏𝒔𝒙𝒚𝒙̅𝑿̅ was found to be more efficient than the estimators proposed by Robson (1957), Singh (1989), Dubey (1993) and Sharma et al., (2007). The percent relative efficiency of the proposed estimator with respect to the conventional estimator and the estimators proposed by Robson (1957), Singh (1989), Dubey (1993) and Sharma et al., (2007) was found to lie in the range of 105.25 to 332.65.