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All Conditional Distributions for Y Given X that are Compatible with a Given Conditional Distribution for X Given Y

Author

Listed:
  • Barry C. Arnold

    (University of California)

  • B. G. Manjunath

    (University of Hyderabad)

Abstract

For a given conditional distribution for X given Y, it is important to identify the class of all conditional distributions for Y given X such that there exists at least one bivariate distribution with the given particular conditional densities. Such problems are addressed as dealing with “compatibility” of two conditional distributions. In the present note our goal is to identify all possible conditional densities for Y given X that are compatible with the given family of distributions of X given Y.

Suggested Citation

  • Barry C. Arnold & B. G. Manjunath, 2022. "All Conditional Distributions for Y Given X that are Compatible with a Given Conditional Distribution for X Given Y," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 419-426, August.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:2:d:10.1007_s13171-020-00200-9
    DOI: 10.1007/s13171-020-00200-9
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    References listed on IDEAS

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    1. Berti, Patrizia & Dreassi, Emanuela & Rigo, Pietro, 2014. "Compatibility results for conditional distributions," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 190-203.
    2. Gourieroux, Christian & Monfort, Alain, 1979. "On the characterization of a joint probability distribution by conditional distributions," Journal of Econometrics, Elsevier, vol. 10(1), pages 115-118, April.
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