A Characterization of Exponential Family Distributions by Expectation of the Sufficient Statistics.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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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
- Statistics and Probability