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Optimum Stratification of a Skewed Population

Authors: D.K. Rao, M.G.M. Khan, K.G. Reddy

Abstract:

The focus of this paper is to develop a technique of solving a combined problem of determining Optimum Strata Boundaries(OSB) and Optimum Sample Size (OSS) of each stratum, when the population understudy isskewed and the study variable has a Pareto frequency distribution. The problem of determining the OSB isformulated as a Mathematical Programming Problem (MPP) which is then solved by dynamic programming technique. A numerical example is presented to illustrate the computational details of the proposed method. The proposed technique is useful to obtain OSB and OSS for a Pareto type skewed population, which minimizes the variance of the estimate of population mean.

Keywords: stratified sampling, optimum strata boundaries, optimum sample size, pareto distribution, dynamic programming technique, Mathematical programming problem

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337065

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[1] Amini, A.A., Weymouth, T.E., and Jain, R.C. (1990). Using Dynamic Programming for Solving Variational Problemsin Vision.IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(9), 855-867.
[2] Bellman, R.E. (1957). Dynamic Programming. Princetown University Press, New Jersey.
[3] Dalenius, T. (1950). The problem of optimum stratification-II. Skand. Aktuartidskr, 33, 203-213.
[4] Dalenius, T., and Gurney, M. (1951). The problem of optimum stratification. Skand. Aktuartidskr, 34, 133-148.
[5] Dalenius, T., and Hodges, J.L. (1959). Minimum variance stratification. Journal of the American Statistical Association, 54, 88-101.
[6] Ekman, G. (1959). Approximate expression for conditional mean and variance over small intervals of a continuous distribution. Annals of the Institute of Statistical Mathematics, 30, 1131-1134.
[7] Gunning, P and Horgan J.M. (2004) A New Algorithm for the Construction of Stratum Boundaries in Skewed Populations. Survey Methodology, 30(2), 159-166.
[8] Hillier, F.S., and Lieberman, G.J. (2010). Introduction to Operations Research. McGraw-Hill, New York.
[9] Khan, E.A., Khan, M.G.M., and Ahsan, M.J. (2002). Optimum stratification: A mathematical programming approach. Culcutta Statistical Association Bulletin, 52 (special), 205-208.
[10] Khan, M.G.M., Najmussehar, and Ahsan, M.J. (2005). Optimum stratification for exponential study variable under Neyman allocation. Journal of Indian Society of Agricultural Statistics, 59(2), 146-150.
[11] Khan, M.G.M., Nand, N., and Ahmad, N. (2008). Determining the optimum strata boundary points using dynamic programming. Survey Methodology, 34(2), 205-214.
[12] Khan, M.G.M.; Rao, D.; Ansari, A.H. and Ahsan, M.J. (2013). Determining Optimum Strata Boundaries and Sample Sizes for Skewed Population with Log-normal Distribution. Journal of Communications in Statistics - Simulation and Computation. DOI: 10.1080/03610918.2013.819917 (To appear).
[13] Kozak, M. (2004). Optimal stratification using random search method in agricultural surveys. Statistics in Transition, 6(5), 797-806.
[14] Lavalle, P. and Hidiroglou, M. (1988). On the stratification of skewed populations. Survey Methodology, 14, 33-43.
[15] Lednicki, B. and Wieczorkowski, R. (2003). Optimal stratification and sample allocation between subpopulations and strata. Statistics in Transition, 6, 287-306.
[16] Mahalanobis, P.C. (1952). Some aspects of the design of sample surveys. Sankhya, 12, 1-7.
[17] Rivest, L.P. (2002). A generalization of Lavalle and Hidiroglou algorithm for stratification in business survey. Survey Methodology, 28, 191-198.
[18] Sethi, V.K. (1963). A note on optimum stratification of population for estimating the population mean. Australian Journal of Statistics, 5, 20-33.