Determining optimum strata boundaries for skewed population with log-normal distribution

Khan, Mohammad G.M. and Rao, Dinesh K. and Ansari, A.H. and Ahsan, M.J. (2011) Determining optimum strata boundaries for skewed population with log-normal distribution. [Conference Proceedings]

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Abstract

The method of choosing the best boundaries that make strata internally homogeneous as far as possible is known as optimum stratification. To achieve this, the strata should be consbucted in such a way that the strata variances for the characteristic under study be as small as possible. If the frequency distribution of the study variable is known, the Optimum Strata Boundaries (OSB) could be obtained by cutting the range of the distribution at suitable points. In this paper the problem of finding the OSB for a skewed population with standard Log-normal distribution is studied. The prohlem is then redefined as the prohlem of determining Optimum Strata Widths (OSW) and is formulated as a Mathematical Programming Problem (MPP) that seeks minimization of the variance of the estimated population
parameter under Neyman allocation subject to the constraint that sum of the widths of all the strata is equal to the total range of the distribution. The formulated MPP tums out to be a multistage decision problem that can be approached by dynamic programming technique. A numerical example is presented to illustrate the application and computational details of the proposed method. The results are compared with the Dalenius and Hodge's cum fi method, which reveals that the proposed technique is more efficient and also useful for a skewed population when the other methods may fail to obtain OSB.

Item Type:	Conference Proceedings
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Technology and Environment (FSTE) > School of Computing, Information and Mathematical Sciences
Depositing User:	Ms Shalni Sanjana
Date Deposited:	11 May 2011 03:08
Last Modified:	15 Mar 2017 22:39
URI:	https://repository.usp.ac.fj/id/eprint/4564

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