Non-exponential families of distributions
- 262 Downloads
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
Unable to display preview. Download preview PDF.
- Barndorff-Nielsen O, Pedersen K (1968) Sufficient data reductions and exponential families. Math Scand 22:197–202Google Scholar
- Barndorff-Nielsen O (1978) Information and exponential families. Wiley, New YorkGoogle Scholar
- Eisenack G, Fenske Ch (1978) Fixpunkttheorie. Bibl Institut, MannheimGoogle Scholar
- Johnson N, Kotz S (1963) Discrete distributions. Wiley, New YorkGoogle Scholar
- Johnson N, Kotz S (1970) Continuous univariate distributions. Wiley, New YorkGoogle Scholar
- Pfanzagl J (1968) A characterization of the one parameter exponential family by existence of uniformly most powerful tests. Sankhyā A 30:147–156Google Scholar