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 CramÂÂ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2008-07-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/10/3/131/ |
| _version_ | 1828146409830875136 |
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| author | Jan Naudts |
| author_facet | Jan Naudts |
| author_sort | Jan Naudts |
| collection | DOAJ |
| 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 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. |
| first_indexed | 2024-04-11T20:47:00Z |
| format | Article |
| id | doaj.art-41d233a5a8fe4559adcde5e4c8c462bb |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-11T20:47:00Z |
| publishDate | 2008-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-41d233a5a8fe4559adcde5e4c8c462bb2022-12-22T04:03:59ZengMDPI 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 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.http://www.mdpi.com/1099-4300/10/3/131/generalised entropymaximum entropy principlevariational principlegeneralised exponential familyBregman divergencegeneralised Fisher informationescort probability. |
| 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. |
| title | 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_short | Generalised Exponential Families and Associated Entropy Functions |
| title_sort | generalised exponential families and associated entropy functions |
| 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 |