Expressions for the Entropy of Binomial-Type Distributions

Expressions for the Entropy of Binomial-Type Distributions. Cheraghchi, M. In Proceedings of the IEEE International Symposium on Information Theory (ISIT), pages 2520–2524, 2018. Extended version in IEEE Transactions on Information Theory.

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We develop a general method for computing logarithmic and log-gamma expectations of distributions. As a result, we derive series expansions and integral representations of the entropy for several fundamental distributions, including the Poisson, binomial, beta-binomial, negative binomial, and hypergeometric distributions. Our results also establish connections between the entropy functions and to the Riemann zeta function and its generalizations.

@INPROCEEDINGS{ref:conf:Che18:entropy,
  author =	 {Mahdi Cheraghchi},
  title =	 {Expressions for the Entropy of Binomial-Type
                  Distributions},
  year =	 2018,
  booktitle =	 {Proceedings of the {IEEE International Symposium on
                  Information Theory (ISIT)}},
  pages =	 {2520--2524},
  note =	 {Extended version in {IEEE Transactions on
                  Information Theory}.},
  doi =		 {10.1109/ISIT.2018.8437888},
  url_Link =	 {https://ieeexplore.ieee.org/document/8437888},
  url_Paper =	 {https://arxiv.org/abs/1708.06394},
  abstract =	 {We develop a general method for computing
                  logarithmic and log-gamma expectations of
                  distributions. As a result, we derive series
                  expansions and integral representations of the
                  entropy for several fundamental distributions,
                  including the Poisson, binomial, beta-binomial,
                  negative binomial, and hypergeometric
                  distributions. Our results also establish
                  connections between the entropy functions and to the
                  Riemann zeta function and its generalizations.  }
}

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