Non-exponential families of distributions
type: Item
instance of: scholarly article
title: Non-exponential families of distributions
zbMATH Open document ID: 0615.62017
DOI: 10.1007/BF01894761
published in: Metrika
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/176068
review text: The problem discussed is whether a given set \({\mathcal P}\) 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-, \(t_ n\)-, logistic-) are not exponential families.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 3996844
zbMATH Keywords: non-exponential families of distributions
zbMATH Keywords: exponential representations
zbMATH Keywords: separation criterion
zbMATH Keywords: t distribution
zbMATH Keywords: logistic distribution
zbMATH Keywords: hyper Poisson
zbMATH Keywords: mutually equivalent probability distributions
zbMATH Keywords: exponential family
zbMATH Keywords: characterization by linear independence
zbMATH Keywords: Cauchy
author: Karl Christoph Klauer
MaRDI profile type: Publication
cites work: Sufficient Data Reduction and Exponential Families.
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description: scientific article; zbMATH DE number 3996844