Optimum Stratification Using Dynamic Programming with a Mixture of Ratio and Product Estimators under Super Population Model

In this study, we have utilized two study variables and one auxiliary variable. The auxiliary variable is used as the stratification variable, and we selected the sample using the stratification variable with a mixture of ratio and product estimators. Under super population set-up, minimal equations have been obtained through minimization of the aggregated variance with the help of the variables under study. The objective function is minimized with respect to the constraints under consideration. The dynamic programming approach has been used to minimize the variance and obtain the optimum strata boundaries. Empirical studies have also been made on the proposed rule utilizing different distributions. A simulation study has been done which shows the gain in precision using the proposed method.