We consider the problem of estimating the finite population mean when some information on auxiliary attribute is available. We obtain the mean square error (MSE) equation for the proposed estimators. It has been shown that the proposed estimator is better than Naik and Gupta (1996), Singh et al. (2008), Abd-Elfattah (2010) estimators. The results have been illustrated numerically by taking some empirical population considered in the literature.
In this paper, we have proposed two log-product -type estimators and a new estimator for estimation of finite population mean under measurement error by using auxiliary information. The expressions for Bias and mean squared error of proposed estimators are evaluated up to first order of approximation. Based on theoretical results obtained, a numerical study by generating Normal population using R programming language is also included to compare the efficiency of proposed estimators with other relevant estimators.
It is experienced that auxiliary information when suitably incorporated yields more efficient and precise estimates. Mishra et al. (2017) have introduced a log type estimator for estimating unknown population mean using ancillary information in simple random sampling. Here we propose an improved log-product type estimator for population variance under double sampling. Properties of the estimators are studied both mathematically and numerically.
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