Estimation of E(Y) from a Population with Known Quantiles

In this paper, we consider the problem of estimating E(Y) based on a simple random sample when at least one of the population quantiles is known. We propose a stratified estimator of E(Y), and show that it is strongly consistent. We then establish the asymptotic normality of the suggested estimator, and prove that it is asymptotically more efficient than the standard mean estimator in simple random sampling. For finite sample sizes, Monte Carlo simulation is used to show that the proposed method considerably improves the standard procedure. Finally, a real data example is used to illustrate the application of the proposed method.