Characterizations of natural exponential families with power variance functions by zero regression properties
type: Item
instance of: scholarly article
title: Characterizations of natural exponential families with power variance functions by zero regression properties
zbMATH Open document ID: 0614.62009
DOI: 10.1007/BF00960071
author: Shaul K. Bar-Lev
author: O. Stramer
publication date: 1987-01-01T00:00:00Z
review text: 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 by the first author and \textit{P. Enis} [Reproducibility and natural exponential families with power variance functions. Ann. Stat. 14, 1507-1522 (1986)] in the context of an investigation of reproducible 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.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 3994727
zbMATH Keywords: characterizations
zbMATH Keywords: zero regression properties
zbMATH Keywords: natural exponential families
zbMATH Keywords: power variance functions
zbMATH Keywords: reproducible exponential families
zbMATH Keywords: normal
zbMATH Keywords: Poisson-type
zbMATH Keywords: gamma
zbMATH Keywords: families generated by stable distributions
zbMATH Keywords: inverse Gaussian
zbMATH Keywords: modified Bessel-type
zbMATH Keywords: Whittaker-type distributions
zbMATH Keywords: compound Poisson
zbMATH Keywords: cumulants
MaRDI profile type: Publication
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3994727