Next Article in Journal
Information Equation of State
Next Article in Special Issue
Modeling Non-Equilibrium Dynamics of a Discrete Probability Distribution: General Rate Equation for Maximal Entropy Generation in a Maximum-Entropy Landscape with Time-Dependent Constraints
Previous Article in Journal / Special Issue
Incremental Entropy Relation as an Alternative to MaxEnt
Article Menu

Article Versions

Export Article

Open AccessArticle
Entropy 2008, 10(3), 131-149; doi:10.3390/entropy-e10030131

Generalised Exponential Families and Associated Entropy Functions

Department of Physics, University of Antwerpen, Groenenborgerlaan 171, 2020 Antwerpen, Belgium
Received: 26 February 2008 / Revised: 1 July 2008 / Accepted: 14 July 2008 / Published: 16 July 2008
Download PDF [213 KB, uploaded 24 February 2015]

Abstract

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 Cram´er and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.
Keywords: generalised entropy; maximum entropy principle; variational principle; generalised exponential family; Bregman divergence; generalised Fisher information; escort probability. generalised entropy; maximum entropy principle; variational principle; generalised exponential family; Bregman divergence; generalised Fisher information; escort probability.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Naudts, J. Generalised Exponential Families and Associated Entropy Functions. Entropy 2008, 10, 131-149.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Entropy EISSN 1099-4300 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top