Optimum stratification for stratified PPSWR sampling design under a model based allocation

Abstract

In this article we consider the problem of finding optimum points of stratification (OPS), based on an auxiliary variable which is highly correlated with study variable, for a model-based allocation, under stratified probability proportional to size with replacement (PPSWR) sampling design. The known model-based allocation used here is an available allocation in earlier literature which was obtained by the authors of the same under a superpopulation model in PPSWR sampling design. Therefore, in this paper, we use the same sampling design and superpopulation model used by them in dealing with problems of finding OPS. Equations for obtaining the OPS have been obtained. It is fascinating to discover that of all hitherto stratification methods developed under PPSWR sampling design for stratifying heteroscedastic populations which are available in literature, our proposed method has come out to be the most brief and easiest to use as OPSs, by this proposed method, are given by geometric means of means of consecutive strata. Although this method is application friendly, it is implicit; therefore alternative methods of finding approximately optimum points of stratification (AOPS) have also been obtained. The efficiencies of all the proposed methods of stratification are examined by using two randomly chosen live populations. The proposed methods of stratification are found to be efficient and suitable for practical applications.