On the joint distribution of two discrete random variables

  • John Panaretos


LetX, Y be two discrete random variables with finite support andXY. Suppose that the conditional distribution ofY givenX can be factorized in a certain way. This paper provides a method of deriving the unique form of the marginal distribution ofX (and hence the joint distribution of (X, Y)) when partial independence only is assumed forY andX−Y.

AMS 1979 subject classification


Key words and phrases

Conditional distribution power series distribution binomial distribution characterization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Chatterji, S. K. (1963). Some elementary characterizations of the Poisson distribution,Amer. Math. Monthly,70, 958–964.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Moran, P. A. P. (1952). A characteristic property of the Poisson distribution,Proc. Camb. Phil. Soc.,48, 206–207.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Panaretos, J. (1979). On characterizing some discrete distributions using an extension of the Rao-Rubin theorem, to appear inSankhyà.Google Scholar
  4. [4]
    Patil, G. P. and Ratnaparkhi, M. V. (1975). Problems of damaged random variables and related characterizations,Statist. Distrib. in Scient. Work, Vol. 3 (eds. G. P. Patil, S. Kotz and J. K. Ord), D. Reidal Publ. Co., Utrecht, 255–270.Google Scholar
  5. [5]
    Patil, G. P. and Seshadri, V. (1964). Characterization theorems for some univariate discrete distributions,J. Roy. Statist. Soc., B,26, 286–292.zbMATHGoogle Scholar
  6. [6]
    Rao, C. R. and Rubin, H. (1964). On a characterization of the Poisson distribution,Sankhyà, A,26, 295–298.MathSciNetzbMATHGoogle Scholar
  7. [7]
    Shanbhag, D. N. (1977). An extension of the Rao-Rubin characterization of the Poisson distribution,J. Appl. Prob.,14, 640–646.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Shanbhag, D. N. and Panaretos, J. (1979). Some results related to the Rao-Rubin characterization of the Poisson distribution,Aust. J. Statist.,21, 78–83.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Shanbhag, D. N. and Taillie, C. (1980). An extension of the Patil-Taillie characterization of the Poisson distribution, to appear inSankhyà.Google Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1981

Authors and Affiliations

  • John Panaretos
    • 1
  1. 1.Trinity CollegeDublin

Personalised recommendations