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1 results

  • On a characterization of Poisson distributions

  • J. Aczél
  • Journal:
    Journal of Applied Probability / Volume 9 / Issue 4 / December 1972
    Published online by Cambridge University Press:
    14 July 2016, pp. 852-856
    Print publication:
    December 1972

  • The conjecture pronounced at the end of the paper of Srivastava and Srivastava (1970) is proved in this paper. It gives the following characterization of (bivariate) Poisson distributions. Suppose that items of two types have been observed certain numbers of times, but these original observations have been reduced due to a destructive process which is the product of two binomial distributions and that the probabilities of these reduced numbers are the same whether damaged or undamaged. Then the original random variables had a bivariate Poisson distribution with zero mutual dependence coefficient.