Accession Number : AD0757022

Title :   A Characterization of Exponential Family Distributions by Expectation of the Sufficient Statistics.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : Sampson,Allan R.

Report Date : FEB 1973

Pagination or Media Count : 16

Abstract : It is shown that if T bar has an unknown exponential family distribution with natural parameter (theta bar), then (G bar) = ET uniquely specifies the moment generating function of T bar. Conversely, it is proved that if T bar is a random variable with a moment generating function of a prescribed form, then it has an exponential family distribution. These results are used to characterize the Normal, Poisson, Bernoulli and Wishart distributions, among others. (Author)

Descriptors :   (*STATISTICAL DISTRIBUTIONS, MOMENTS), PROBABILITY DENSITY FUNCTIONS, RANDOM VARIABLES, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE