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On optimum stratification with proportional allocation for a class of pareto distributions

Aggarwal, V and Singnh, R (1984) On optimum stratification with proportional allocation for a class of pareto distributions. In: Communication in statistics-theory and methods, 13 (24). pp. 3107-3116.

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Cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0001.gif rule [Singh (1975)] has been suggested in the literature for finding approximately optimum strata boundaries for proportional allocation, when the stratification is done on the study variable. This paper shows that for the class of density functions arising from the Wang and Aggarwal (1984) representation of the Lorenz Curve (or DBV curves in case of inventory theory), the cum ./LSTA_A_8828879_O_XML_IMAGES/LSTA_A_8828879_O_ILM0002.gif rule in place of giving approximately optimum strata boundaries, yields exactly optimum boundaries. It is also shown that the conjecture of Mahalanobis (1952) “. . .an optimum or nearly optimum solutions will be obtained when the expected contribution of each stratum to the total aggregate value of Y is made equal for all strata” yields exactly optimum strata boundaries for the case considered in the paper.

Item Type: Journal Article
Publication: Communication in statistics-theory and methods
Publisher: Marcel Dekker Inc
Additional Information: Copyright of this article belongs to Marcel Dekker Inc.
Keywords: minimal equations; lorenz curve; optimum strata boundaries; egalitarian line; aggregage value
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 09 Feb 2010 10:58
Last Modified: 09 Feb 2010 10:58
URI: http://eprints.iisc.ac.in/id/eprint/20036

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