Accession Number : AD0712758

Title :   A CHARACTERIZATION OF THE POISSON DISTRIBUTION BASED ON RANDOM SPLITTING AND RANDOM EXPANDING.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Wang,Peter C. C.

Report Date : 12 AUG 1970

Pagination or Media Count : 21

Abstract : Let X be a discrete random variable with parameter lambda = E(x)< infinity and denote B(n,r,a) = (sup n, sub r)(a to the power r)((1-a) to the power (m-r)). Let the distribution of X be compounded with B(n,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)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, THEOREMS), EXPONENTIAL FUNCTIONS, RANDOM VARIABLES, PROBABILITY, INVARIANCE

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE