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Characterizations of natural exponential families with power variance functions by zero regression properties
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  • Published: December 1987

Characterizations of natural exponential families with power variance functions by zero regression properties

  • Shaul K. Bar-Lev1 &
  • Osnat Stramer1 

Probability Theory and Related Fields volume 76, pages 509–522 (1987)Cite this article

  • 152 Accesses

  • 9 Citations

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Summary

Series of new characterizations by zero regression properties are derived for the distributions in the class of natural exponential families with power variance functions. Such a class of distributions has been introduced in Bar-Lev and Enis (1986) in the context of an investigation of reproductible exponential families. This class is broad and includes the following families: normal, Poisson-type, gamma, all families generated by stable distributions with characteristic exponent an element of the unit interval (among these are the inverse Gaussian, Modified Bessel-type, and Whittaker-type distributions), and families of compound Poisson distributions generated by gamma variates. The characterizations by zero regression properties are obtained in a unified approach and are based on certain relations which hold among the cumulants of the distributions in this class. Some remarks are made indicating how the techniques used here can be extended to obtain characterizations of general exponential families.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Haifa, 31999, Haifa, Israel

    Shaul K. Bar-Lev & Osnat Stramer

Authors
  1. Shaul K. Bar-Lev
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  2. Osnat Stramer
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Additional information

The work of this author was performed while he was a visitor in the Department of Statistics, State University of New York at Buffalo

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Bar-Lev, S.K., Stramer, O. Characterizations of natural exponential families with power variance functions by zero regression properties. Probab. Th. Rel. Fields 76, 509–522 (1987). https://doi.org/10.1007/BF00960071

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  • Received: 03 July 1985

  • Revised: 25 July 1987

  • Issue Date: December 1987

  • DOI: https://doi.org/10.1007/BF00960071

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Keywords

  • Stochastic Process
  • Probability Theory
  • Poisson Distribution
  • Mathematical Biology
  • Variance Function
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