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Biometrika 1968 55(1):179-188; doi:10.1093/biomet/55.1.179
© 1968 by Biometrika Trust
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Contingency tables with given marginals

C. T. IRELAND and S. KULLBACK

The George Washington University

In its simplest formulation the problem considered is to estimate the cell probabilities Pij of an r × c contingency table for which the marginal probabilities Pi and Pj are known and fixed, so as to minimize {Sigma}{Sigma}pij In (pij/{pi}ij), where {pi}ij are the corresponding entries in a given contingency table. An iterative procedure is given for determining the estimates and it is shown that the estimates are BAN, and that the iterative procedure is convergent. A summary of results for a four-way contingency table is given. An illustrative example is given.


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