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Specification of distributions by combinations of marginal and conditional distributions

Author

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  • Arnold, Barry C.
  • Castillo, Enrique
  • Sarabia, José María

Abstract

A k-dimensional density function is determined by certain combinations of marginal and conditional densities. The present paper identifies all possible such specifications. Gelman and Speed (1993) have treated the finite discrete case of this problem. The present paper extends their work to a more general setting. Appropriate compatibility conditions are described as are sufficient conditions for uniqueness of the resulting density which must, in general, be checked for integrability. An example of the application of the conditions is included.

Suggested Citation

  • Arnold, Barry C. & Castillo, Enrique & Sarabia, José María, 1996. "Specification of distributions by combinations of marginal and conditional distributions," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 153-157, February.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:2:p:153-157
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Gramer Erhard, 2000. "Probability Measures With Given Marginals And Conditionals: I-Projections And Conditional Iterative Proportional Fitting," Statistics & Risk Modeling, De Gruyter, vol. 18(3), pages 311-330, March.
    2. Cramer, Erhard, 1998. "Conditional Iterative Proportional Fitting for Gaussian Distributions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 261-276, May.
    3. Ip, Edward H. & Wang, Yuchung J., 2009. "Canonical representation of conditionally specified multivariate discrete distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(6), pages 1282-1290, July.
    4. 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.
    5. Castillo, Enrique & Gutiérrez, José Manuel & Hadi, Ali S., 1998. "Modeling Probabilistic Networks of Discrete and Continuous Variables," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 48-65, January.

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