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Construction of Optimum Strata Boundaries for Uniform and Exponential Auxiliary Variable |
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PP: 37-43 |
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doi:10.18576/amisl/060105
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Author(s) |
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Faizan Danish,
S. E. H. Rizvi,
Manish Kr. Sharma,
M. Iqbal Jeelani,
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Abstract |
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| The main objective of stratification is to give a better cross section of the population so as to gain a higher degree of relative precision which is possible only when we have the best way of stratification. In this paper, we discuss the problem of determining the OSB of a study variable based on auxiliary variable under proportional allocation. The problem is formulated as a Mathematical Programming Problem (MPP) which minimizes the objective function subject to the constraint that the sum of the widths of all the strata is equal to the whole range of the distribution. The distributions of the auxiliary variable are considered continuous with uniform and exponential density functions separately. The formulated MPPs, which turn out to be multistage decision problems, could then be solved using dynamic programming approach. The theoretical results have been illustrated empirically for both the distributions which show that there is substantial gain in efficiency with the increase in the number of strata.
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