A Characterization of Exponential Family Distributions by Expectation of the Sufficient Statistics.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1973
- Accession Number
- AD0757022
Entities
People
- Allan R. Sampson
Organizations
- Florida State University