Characterizations of natural exponential families with power variance functions by zero regression properties
 Shaul K. BarLev,
 Osnat Stramer
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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 BarLev and Enis (1986) in the context of an investigation of reproductible exponential families. This class is broad and includes the following families: normal, Poissontype, gamma, all families generated by stable distributions with characteristic exponent an element of the unit interval (among these are the inverse Gaussian, Modified Besseltype, and Whittakertype 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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 Title
 Characterizations of natural exponential families with power variance functions by zero regression properties
 Journal

Probability Theory and Related Fields
Volume 76, Issue 4 , pp 509522
 Cover Date
 19871201
 DOI
 10.1007/BF00960071
 Print ISSN
 01788051
 Online ISSN
 14322064
 Publisher
 SpringerVerlag
 Additional Links
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 Authors

 Shaul K. BarLev ^{(1)}
 Osnat Stramer ^{(1)}
 Author Affiliations

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