Obtaining Strata Boundaries under Proportional Allocation with Varying Cost of Every Unit

Faizan Danish, S.E.H. Rizvi, M. Iqbal Jeelani, Javaid Ahmad Reashi

Abstract


One of the main reasons for stratifying the population is to produce a gain in precision of the estimates, in the sample surveys. For achieving this, one of the problem is determination of optimum strata boundaries. The strata boundaries should be obtained in such a way, so that it can reasonably expect to reduce the cost of the survey as much as possible without sacrificing the accuracy or alternatively, reducing the margin of error to the greatest possible extent for the same expected cost. In this paper, we have discussed the way of obtaining optimum strata boundaries when the cost of every unit varies in the whole strata. The problem is formulated as non-linear programming problem which is solved by using Bellman’s principle of optimality. For numerical illustration an example is presented for uniformly distributed study variable.


Keywords


Optimum strata boundaries, Non-linear programming problem, Bellman’s principle of optimality.

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DOI: http://dx.doi.org/10.18187/pjsor.v13i3.1719

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Title

Obtaining Strata Boundaries under Proportional Allocation with Varying Cost of Every Unit

Keywords

Optimum strata boundaries, Non-linear programming problem, Bellman’s principle of optimality.

Description

One of the main reasons for stratifying the population is to produce a gain in precision of the estimates, in the sample surveys. For achieving this, one of the problem is determination of optimum strata boundaries. The strata boundaries should be obtained in such a way, so that it can reasonably expect to reduce the cost of the survey as much as possible without sacrificing the accuracy or alternatively, reducing the margin of error to the greatest possible extent for the same expected cost. In this paper, we have discussed the way of obtaining optimum strata boundaries when the cost of every unit varies in the whole strata. The problem is formulated as non-linear programming problem which is solved by using Bellman’s principle of optimality. For numerical illustration an example is presented for uniformly distributed study variable.


Date

2017-09-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 13 No. 3, 2017



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810