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A Mathematical Programming Approach For Obtaining Optimum Strata Boundaries Using Two Auxiliary Variables Under Proportional Allocation

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  • Danish Faizan

    (Division of Statistics and Computer Science, Faculty of Basic Sciences, SKUAST-Jammu, Main campus, Chatha, ; India)

Abstract

Optimum stratification is the method of choosing the best boundaries that make the strata internally homogenous. Many authors have attempted to determine the optimum strata boundaries (OSB) when a study variable is itself a stratification variable. However, in many practical situations fetching information regarding the study variable is either difficult or sometimes not available. In such situations we find help in the variable (s) closely related to the study variable. Using auxiliary information many authors have formulated the problem as a MPP by redefining the problem as the problem of optimum strata width, and developed a solution procedure using dynamic programming technique. By using many distributions they worked out the optimum strata boundary points for the population under different allocation. In this paper, under proportional allocation OSBs are determined for the study variable using two auxiliary variables as the basis of stratification with uniform, right-triangular, exponential and lognormal frequency distribution by formulating the problems which are executed by using dynamic programming. Empirical studies are presented to illustrate the computation details of the solution procedure and its comparison with the existing literature.

Suggested Citation

  • Danish Faizan, 2018. "A Mathematical Programming Approach For Obtaining Optimum Strata Boundaries Using Two Auxiliary Variables Under Proportional Allocation," Statistics in Transition New Series, Polish Statistical Association, vol. 19(3), pages 507-526, September.
    • Handle: RePEc:vrs:stintr:v:19:y:2018:i:3:p:507-526:n:2
    DOI: 10.21307/stattrans-2018-028
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    References listed on IDEAS

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    1. I. Thomsen, 1976. "A comparison of approximately optimal stratification given proportional allocation with other methods of stratification and allocation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 23(1), pages 15-25, December.
    2. W. Bühler & T. Deutler, 1975. "Optimal stratification and grouping by dynamic programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 22(1), pages 161-175, December.
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