ESTIMATION OF DISTRIBUTION FUNCTION AND MEDIAN IN TWO PHASE SAMPLING

Abstract

In this paper, we consider the problem of estimating the distribution function of a random variable in a finite population using two phase sampling, which is an extension of recent work by Singh, Joarder and Tracy (2001). Besides, three types of estimators for estimating the median are also considered. The variances of the proposed estimators are minimised for a fixed total cost and the expressions for the optimum values of the first and second phase sample sizes are obtained. Numerical illustrations are also given to have an idea about the relative efficiency of the proposed estimators of the median over the usual one for the fixed total cost.