• DocumentCode
    756127
  • Title

    On the Maximum Entropy Properties of the Binomial Distribution

  • Author

    Yu, Yaming

  • Author_Institution
    Dept. of Stat., Univ. of California, Irvine, CA
  • Volume
    54
  • Issue
    7
  • fYear
    2008
  • fDate
    7/1/2008 12:00:00 AM
  • Firstpage
    3351
  • Lastpage
    3353
  • Abstract
    It is shown that the Binomial(n,p) distribution maximizes the entropy in the class of ultra-log-concave distributions of order n with fixed mean np. This result, which extends a theorem of Shepp and Olkin (1981), is analogous to that of Johnson (2007), who considers the Poisson case. The proof constructs a Markov chain whose limiting distribution is Binomial(n,p) and shows that the entropy never decreases along the iterations of this Markov chain.
  • Keywords
    Markov processes; Poisson distribution; binomial distribution; maximum entropy methods; Markov chain; Poisson case; binomial distribution; maximum entropy properties; ultra log concave distributions; Bernoulli sum; Markov chain; hypergeometric thinning; ultra-log-concavity;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/TIT.2008.924715
  • Filename
    4545002
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=756127