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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?)

  • Albert W. Marshall and Ingram Olkin, Inequalities: theory of majorization and its applications, Mathematics in Science and Engineering, vol. 143, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 552278
  • P. S. Matveev, The entropy of the multinomial distribution, Teor. Verojatnost. i Primenen. 23 (1978), no. 1, 196–198 (Russian, with English summary). MR 0490451
  • L. A. Shepp and I. Olkin, Entropy of the sum of independent Bernoulli random variables and of the multinomial distribution, Contributions to probability, Academic Press, New York-London, 1981, pp. 201–206. MR 618689

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Article copyright: © Copyright 1989 American Mathematical Society