On the joint distribution of two discrete random variables
LetX, Y be two discrete random variables with finite support andX≧Y. 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 classification60E05
Key words and phrasesConditional distribution power series distribution binomial distribution characterization
Unable to display preview. Download preview PDF.
- Panaretos, J. (1979). On characterizing some discrete distributions using an extension of the Rao-Rubin theorem, to appear inSankhyà.Google Scholar
- 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
- Shanbhag, D. N. and Taillie, C. (1980). An extension of the Patil-Taillie characterization of the Poisson distribution, to appear inSankhyà.Google Scholar