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An entropy inequality for the bi-multivariate hypergeometric distribution


Authors: Fred Kochman, Alan Murray and Douglas B. West
Journal: Proc. Amer. Math. Soc. 107 (1989), 479-485
MSC: Primary 60E05; Secondary 94A17
DOI: https://doi.org/10.1090/S0002-9939-1989-0979050-8
MathSciNet review: 979050
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Abstract: Given parameters $ \bar r = {r_1}, \ldots ,{r_m}$ and $ \bar c = {c_1}, \ldots ,{c_n}$ with $ \sum {{r_i}} = \sum {{c_j}} = N$, the bi-multivariate hypergeometric distribution is the distribution on nonnegative integer $ m \times n$ matrices with row sums $ \bar r$ and column sums $ \bar c$ defined by $ {\text{Prob}}\left( A \right) = \prod {{r_i}} !\prod {{c_j}} ! / \left( {N!\prod {{a_{ij}}!} } \right)$. It is shown that the entropy of this distribution is a Schur-concave function of the block-size parameters.


References [Enhancements On Off] (What's this?)

  • [1] A. W. Marshall and I. Olkin, Inequalities: theory of majorization and its applications, Academic Press, New York City, 1979. MR 552278 (81b:00002)
  • [2] P. S. Mateev, The entropy of the multinomial distribution (Russian. English summary.), Teor. Verojatnost. i Primenen 23 (1978), 196-198. MR 0490451 (58:9796)
  • [3] L. A. Shepp and I. Olkin, Entropy of the sum of independent Bernoulli random variables and of the multinomial distribution, in Contributions to Probability, Academic Press, New York City, 1981, 201-206. MR 618689 (82g:60031)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1989-0979050-8
Article copyright: © Copyright 1989 American Mathematical Society

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