Some improved ratio type estimators of population mean and ratio in finite population sample surveys

In this paper we present a class of ratio type estimators of the population mean and ratio in a finite population sample surveys with without replacement simple random sampling design, where information on an auxiliary variate x positively correlated with the main variate y is available. Large sample approximations to mean square errors (MSE) of these estimatorsare evaluated and their MSE's are compared with the MSE of the usual ratio estimator [ybar]_R of [ybar] the population mean of y. It is shown that under certain conditions these estimators are more efficient than [ybar]_R. When a prior knowledge of the value of thecoefficient of variation, c_y, of y is at hand, ratio type estimator, say [ybar]₁ of [ybar] is proposed. It is shown, under certain conditions, that [ybar]₁ is more efficient than [ybar]_R. When values of c_y, c_x and the population correlation coefficient ρ is at hand, then we have proposed another estimator, say [ybar]₂ of [ybar], which is always better than [ybar]_R as far as the efficiency is concerned. In fact, is [ybar] ₂ is shown to be even better than [ybar]₁. Finally estimators better than the usual ratio estimator [ybar]/[xbar] of [Ybar] are given.

Keywords

• Population mean,
• population ratio,
• auxilary variate,
• prior information,
• ratio estimator,
• ratio type estimators