Optimum Stratiﬁcation of a Skewed Population
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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1337065Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3722
 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.
 Bellman, R.E. (1957). Dynamic Programming. Princetown University Press, New Jersey.
 Dalenius, T. (1950). The problem of optimum stratiﬁcation-II. Skand. Aktuartidskr, 33, 203-213.
 Dalenius, T., and Gurney, M. (1951). The problem of optimum stratiﬁcation. Skand. Aktuartidskr, 34, 133-148.
 Dalenius, T., and Hodges, J.L. (1959). Minimum variance stratiﬁcation. Journal of the American Statistical Association, 54, 88-101.
 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.
 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.
 Hillier, F.S., and Lieberman, G.J. (2010). Introduction to Operations Research. McGraw-Hill, New York.
 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.
 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.
 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.
 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).
 Kozak, M. (2004). Optimal stratiﬁcation using random search method in agricultural surveys. Statistics in Transition, 6(5), 797-806.
 Lavalle, P. and Hidiroglou, M. (1988). On the stratiﬁcation of skewed populations. Survey Methodology, 14, 33-43.
 Lednicki, B. and Wieczorkowski, R. (2003). Optimal stratiﬁcation and sample allocation between subpopulations and strata. Statistics in Transition, 6, 287-306.
 Mahalanobis, P.C. (1952). Some aspects of the design of sample surveys. Sankhya, 12, 1-7.
 Rivest, L.P. (2002). A generalization of Lavalle and Hidiroglou algorithm for stratiﬁcation in business survey. Survey Methodology, 28, 191-198.
 Sethi, V.K. (1963). A note on optimum stratiﬁcation of population for estimating the population mean. Australian Journal of Statistics, 5, 20-33.