Performance of an Estimator for Estimating Population Mean Using Simple and Stratified Random Sampling

Abstract

In the present study, we have suggested an improved class of estimator for estimating populating mean with the help of two auxiliary variable using simple random sampling and stratified random sampling. We have derived the mean square error and bias of the suggested estimator, and theoretically showed that our proposed estimator performs better than some given existing estimators. In addition, we support this theoretical result with the help of numerical examples. 1. SOME ESTIMATORS UNDER SIMPLE RANDOM SAMPLING In the theory of sample survey, we can increase the precision or accuracy of suggested estimator by using auxiliary information but when no additional information related to auxiliary variable is available then the simplest estimator of population mean is the sample mean. When study variable Y is highly positively correlated with the auxiliary variable(X) then we use ratio estimator; when it is negatively correlated then we use product estimator for estimating population parameters. In large scale survey, we often collect data on more than one auxiliary variable(s) and some of these may be correlated with y. (1), (2), (3), (4), Dianna and Perri(2007), Singh et al. (2011), (5), Malik and Singh (5, 6), Singh and Singh (7) considered some estimators which utilised information on several auxiliary variables which are correlated with the study variable. Bahl and Tuteja (8) suggested an exponential ratio type estimator. Singh (9) proposed a ratio cum product type estimator. Kadilar and Cingi(10) have proposed ratio in difference type estimator. Motivated by these authors we have suggested an improved different type of estimator for estimating population mean using simple and stratified random sampling. For the different choices of constants different family and some well-known existing estimators may be generated from the proposed family of estimators.