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On Compatibility/Incompatibility of Two Discrete Probability Distributions in the Presence of Incomplete Specification

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  • Indranil Ghosh

    (University of North Carolina)

  • N. Balakrishnan

    (McMaster University)

Abstract

Conditional specification of distributions is a developing area with several applications. In the finite discrete case, a variety of compatible conditions can be derived. In this paper, we revisit a rank–based criterion for identifying compatible distributions corresponding to complete conditional specification, including the case with zeros under the finite discrete set up. Based on this, we primarily focus on the compatibility of two conditionals (under the finite discrete set-up) in which incomplete specification on either or both the conditional matrices are present. Compatibility in the general case are also briefly discussed. The proposed methods are finally illustrated with several examples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00243-6
    DOI: 10.1007/s13171-021-00243-6
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    References listed on IDEAS

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    1. Barry Arnold & D. Gokhale, 1998. "Distributions most nearly compatible with given families of conditional distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 377-390, December.
    2. 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.
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    4. Wesolowski, J., 1995. "Bivariate Discrete Measures via a Power Series Conditional Distribution and a Regression," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 219-229, November.
    5. Indranil Ghosh & Saralees Nadarajah, 2016. "An alternative approach for compatibility of two discrete conditional distributions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(15), pages 4416-4432, August.
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