Non-exponential families of distributions
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The problem discussed is whether a given setP of mutually equivalent probability distributions constitutes an exponential family or not. As an alternative to the well known characterization by linear independence an analytic method is pointed out which allows one to demonstrate in a relatively easy way that many familiar classes of distributions (e.g. Cauchy-,tn-, logistic-) are not exponential families.
Key words and PhrasesExponential families exponential representations minimal statistics
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