Heuristic Algorithm for Obtaining Approximate Optimum Stratification with Mixture of Ratio and Product Estimators

Abstract

In this investigation, we examined the impact of employing simple random sampling on the stratification points pertaining to the two independent variables. The study focused on a variable (X) exhibiting a robust correlation, and we employed a combination of ratio and product estimators to select a representative sample and establish the population mean. By maintaining a comprehensive superpopulation framework, we successfully identified concise equations that effectively reduced the overall variability within the dataset. To reveal the underlying nature of these mathematical derivations, we employed the cumulative cube roots rule to determine nearly optimal stratification points for the two research variables. The validity of this suggested rule was assessed through rigorous testing utilizing empirical and simulated data obtained from diverse distributions.