Many common probability distributions in statistics like the Gaussian,
multinomial, Beta or Gamma distributions can be studied under the unified
framework of exponential families. In this paper, we prove that both Rényi
and Tsallis divergences of distributions belonging to the same exponential
family admit a generic closed form expression. Furthermore, we show that
Rényi and Tsallis entropies can also be calculated in closed-form for
sub-families including the Gaussian or exponential distributions, among others.
Описание
[1105.3259] On Rényi and Tsallis entropies and divergences for exponential families
%0 Journal Article
%1 nielsen2011renyi
%A Nielsen, Frank
%A Nock, Richard
%D 2011
%K bayesian divergences entropy
%R 10.1088/1751-8113/45/3/032003
%T On Rényi and Tsallis entropies and divergences for exponential
families
%U http://arxiv.org/abs/1105.3259
%X Many common probability distributions in statistics like the Gaussian,
multinomial, Beta or Gamma distributions can be studied under the unified
framework of exponential families. In this paper, we prove that both Rényi
and Tsallis divergences of distributions belonging to the same exponential
family admit a generic closed form expression. Furthermore, we show that
Rényi and Tsallis entropies can also be calculated in closed-form for
sub-families including the Gaussian or exponential distributions, among others.
@article{nielsen2011renyi,
abstract = {Many common probability distributions in statistics like the Gaussian,
multinomial, Beta or Gamma distributions can be studied under the unified
framework of exponential families. In this paper, we prove that both R\'enyi
and Tsallis divergences of distributions belonging to the same exponential
family admit a generic closed form expression. Furthermore, we show that
R\'enyi and Tsallis entropies can also be calculated in closed-form for
sub-families including the Gaussian or exponential distributions, among others.},
added-at = {2019-12-11T14:46:17.000+0100},
author = {Nielsen, Frank and Nock, Richard},
biburl = {https://www.bibsonomy.org/bibtex/2ba479ac3683859218167084e11373aab/kirk86},
description = {[1105.3259] On Rényi and Tsallis entropies and divergences for exponential families},
doi = {10.1088/1751-8113/45/3/032003},
interhash = {9367c87c6eafb9c5fdd0bb9dd07551c6},
intrahash = {ba479ac3683859218167084e11373aab},
keywords = {bayesian divergences entropy},
note = {cite arxiv:1105.3259Comment: 7 pages},
timestamp = {2019-12-11T14:46:37.000+0100},
title = {On R\'enyi and Tsallis entropies and divergences for exponential
families},
url = {http://arxiv.org/abs/1105.3259},
year = 2011
}