Generalised exponential families and associated entropy functions

Details Generalised exponential families and associated entropy functions Generalised exponential families and associated entropy functions

2008-03-02

arxiv.org/abs/0803.0104v1

Physics

Mathematical Physics

20 pages

Scientific paper

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 Cramer and Rao becomes an equality in the case of an exponential family can be generalised. However, this requires the introduction of escort probabilities.

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