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

Generalised Exponential Families and Associated Entropy Functions

Received: 26 February 2008; in revised form: 1 July 2008 / Accepted: 14 July 2008 / Published: 16 July 2008
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
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MDPI and ACS Style

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

AMA Style

Naudts J. Generalised Exponential Families and Associated Entropy Functions. Entropy. 2008; 10(3):131-149.

Chicago/Turabian Style

Naudts, Jan. 2008. "Generalised Exponential Families and Associated Entropy Functions." Entropy 10, no. 3: 131-149.

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