Generalised Exponential Families and Associated Entropy Functions

A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The well-known result that the inequality of CramÃ‚Â...

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Bibliographic Details
Main Author:	Jan Naudts
Format:	Article
Language:	English
Published:	MDPI AG 2008-07-01
Series:	Entropy
Subjects:	generalised entropy maximum entropy principle variational principle generalised exponential family Bregman divergence generalised Fisher information escort probability.
Online Access:	http://www.mdpi.com/1099-4300/10/3/131/

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spelling	doaj-41d233a5a8fe4559adcde5e4c8c462bb2020-11-24T23:23:14ZengMDPI AGEntropy1099-43002008-07-0110313114910.3390/entropy-e10030131Generalised Exponential Families and Associated Entropy FunctionsJan NaudtsA generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The well-known result that the inequality of CramÃ‚Â´er and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.http://www.mdpi.com/1099-4300/10/3/131/generalised entropymaximum entropy principlevariational principlegeneralised exponential familyBregman divergencegeneralised Fisher informationescort probability.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Jan Naudts
spellingShingle	Jan Naudts Generalised Exponential Families and Associated Entropy Functions Entropy generalised entropy maximum entropy principle variational principle generalised exponential family Bregman divergence generalised Fisher information escort probability.
author_facet	Jan Naudts
author_sort	Jan Naudts
title	Generalised Exponential Families and Associated Entropy Functions
title_short	Generalised Exponential Families and Associated Entropy Functions
title_full	Generalised Exponential Families and Associated Entropy Functions
title_fullStr	Generalised Exponential Families and Associated Entropy Functions
title_full_unstemmed	Generalised Exponential Families and Associated Entropy Functions
title_sort	generalised exponential families and associated entropy functions
publisher	MDPI AG
series	Entropy
issn	1099-4300
publishDate	2008-07-01
description	A generalised notion of exponential families is introduced. It is based on the variational principle, borrowed from statistical physics. It is shown that inequivalent generalised entropy functions lead to distinct generalised exponential families. The well-known result that the inequality of CramÃ‚Â´er and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.
topic	generalised entropy maximum entropy principle variational principle generalised exponential family Bregman divergence generalised Fisher information escort probability.
url	http://www.mdpi.com/1099-4300/10/3/131/
work_keys_str_mv	AT jannaudts generalisedexponentialfamiliesandassociatedentropyfunctions
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Generalised Exponential Families and Associated Entropy Functions

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