A CHARACTERIZATION OF THE POISSON DISTRIBUTION BASED ON RANDOM SPLITTING AND RANDOM EXPANDING.
STANFORD UNIV CALIF DEPT OF STATISTICS
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Let X be a discrete random variable with parameter lambda Ex infinity and denote Bn,r,a sup n, sub ra to the power r1-a to the power m-r. Let the distribution of X be compounded with Bn,r,a. If the resulting distribution is governed by the same law as X, then a characterization of the Poisson distribution is obtained. An alternative proof of the Rao-Rubin characterization is provided. Author
- Statistics and Probability