ON SIMPLE RANDOM SAMPLING WITH REPLACEMENT
In simple random sampling with replacement, Basu (1958) and Des Raj and Khamis (1958) showed that for estimating the population mean, the average of distinct units is more efficient than the overall sample mean. In this paper, a detailed treatment of the above problem is given, and the exact expression for the variance of above estimator is derived. The relative efficiency of the above estimator with other estimators is also considered. An improved estimator of the population variance is obtained. Finally, a comparison between the two simple random sampling schemes (with and without replacement) is made.