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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An entropy inequality for the bi-multivariate hypergeometric distribution
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by Fred Kochman, Alan Murray and Douglas B. West PDF
Proc. Amer. Math. Soc. 107 (1989), 479-485 Request permission

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
  • 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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • 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