Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


An entropy inequality for the bi-multivariate hypergeometric distribution
HTML articles powered by AMS MathViewer

by Fred Kochman, Alan Murray and Douglas B. West PDF
Proc. Amer. Math. Soc. 107 (1989), 479-485 Request permission


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.
  • 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
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60E05, 94A17
  • Retrieve articles in all journals with MSC: 60E05, 94A17
Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 479-485
  • MSC: Primary 60E05; Secondary 94A17
  • DOI:
  • MathSciNet review: 979050