OPTIMUM STRATIFICATION FOR AN AUXILIARY VARIABLE OPTIMUM ALLOCATION UNDER A SUPERPOPULATION MODEL

In this paper, the problem of optimum stratification for an auxiliary variable optimum allocation in sampling with simple random sampling with replacement under a superpopulation model is considered. Equations which give optimum points of stratification are obtained and their methods of approximation for finding approximately optimum points of stratification are also derived. Moreover, the general perception that in the computation of optimum allocation unknown proportionate values of sigma(2)(hy) of a study variable y can be replaced by known proportionate values sigma(2)(hx) of a highly correlated auxiliary variable x has been critiqued in this paper particularly when such an allocation is considered for deriving equations for construction of strata; therefore, auxiliary variable optimum allocation, obtained by Hanurav [11] with the assumption that coefficients of variation of auxiliary variable x are the same in all strata, is used in this paper for deriving equations to stratify populations optimally. All the proposed methods of stratification are empirically examined through numerical illustrations in generated populations and are found efficient.