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On uniform marginal representation of contingency tables

Author

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  • Arnold, Barry C.
  • Gokhale, D. V.

Abstract

For a two-dimensional probability distribution represented as a contingency table, an algorithm due to Mosteller (1968) "standardizes" the table to have uniform marginals so as to obtain its "uniform marginals representation (UMR)". In this note, this algorithm is first shown to minimize the Kullback-Leibler information function between distributions with uniform marginals and the given distribution. Next, a characterization of such tables is proved, in terms of (i) their UMRs, (ii) cross-product ratios of each of their 2 x 2 subtables (iii) the ability to obtain one table from another only by adjustment of their row or column marginals.

Suggested Citation

  • Arnold, Barry C. & Gokhale, D. V., 1994. "On uniform marginal representation of contingency tables," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 311-316, November.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:4:p:311-316
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    Cited by:

    1. Chen, Hua Yun, 2010. "Compatibility of conditionally specified models," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 670-677, April.
    2. Wang, Yuchung J. & Kuo, Kun-Lin, 2010. "Compatibility of discrete conditional distributions with structural zeros," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 191-199, January.
    3. Ghosh, Indranil, 2023. "On the issue of convergence of certain divergence measures related to finding most nearly compatible probability distribution under the discrete set-up," Statistics & Probability Letters, Elsevier, vol. 203(C).
    4. Indranil Ghosh & N. Balakrishnan, 2023. "On Compatibility/Incompatibility of Two Discrete Probability Distributions in the Presence of Incomplete Specification," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 274-291, February.
    5. Indranil Ghosh, 2018. "A complete characterization of bivariate densities using the conditional percentile function," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 485-492, July.

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