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Metrika

, Volume 33, Issue 1, pp 299–305 | Cite as

Non-exponential families of distributions

  • K. C. Klauer
Publications

Summary

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 Phrases

Exponential families exponential representations minimal statistics 

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References

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

Copyright information

© Physica-Verlag 1986

Authors and Affiliations

  • K. C. Klauer
    • 1
  1. 1.Institut für Statistik und WirtschaftsmathematikRWTH AachenAachenWest-Germany

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