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A note on inconsistent families of discrete multivariate distributions

Author

Listed:
  • Sugata Ghosh

    (Indian Institute of Technology)

  • Subhajit Dutta

    (Indian Institute of Technology)

  • Marc G. Genton

    (King Abdullah University of Science and Technology)

Abstract

We construct a d-dimensional discrete multivariate distribution for which any proper subset of its components belongs to a specific family of distributions. However, the joint d-dimensional distribution fails to belong to that family and in other words, it is ‘inconsistent’ with the distribution of these subsets. We also address preservation of this ‘inconsistency’ property for the symmetric Binomial distribution, and some discrete distributions arising from the multivariate discrete normal distribution.

Suggested Citation

  • Sugata Ghosh & Subhajit Dutta & Marc G. Genton, 2017. "A note on inconsistent families of discrete multivariate distributions," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-13, December.
    • Handle: RePEc:spr:jstada:v:4:y:2017:i:1:d:10.1186_s40488-017-0061-8
    DOI: 10.1186/s40488-017-0061-8
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    References listed on IDEAS

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    1. Cuadras, C. M., 1992. "Probability distributions with given multivariate marginals and given dependence structure," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 51-66, July.
    2. Dutta, Subhajit & Genton, Marc G., 2014. "A non-Gaussian multivariate distribution with all lower-dimensional Gaussians and related families," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 82-93.
    3. T. Nguyen & A. Gupta & Y. Wang, 1996. "A characterization of certain discrete exponential families," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(3), pages 573-576, September.
    4. Subrata Chakraborty & Dhrubajyoti Chakravarty, 2016. "A new discrete probability distribution with integer support on (−∞, ∞)," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 492-505, January.
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