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Book Review

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Book Information:

Authors: Albert W. Marshall and Ingram Olkin
Title: Inequalities: Theory of majorization and its applications
Additional book information: Mathematics in Science and Engineering, Vol. 143, Academic Press, New York, 1979, xx + 569 pp., $49.50.

Author: Y. L. Tong
Title: Probability inequalities in multivariate distributions
Additional book information: Probability and Mathematical Statistics, A Series of Monographs and Textbooks, Academic Press, New York, 1980, xiii + 239 pp., $ 29.50.

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

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  • 2. S. Das Gupta, M. L. Eaton, I. Olkin, M. D. Perlman, L. J. Savage and M. Sobel, Inequalities on the probability content of convex regions for elliptically contoured distributions, Proc. Sixth Berkeley Sympos. on Math. Statistics and Probability (Berkeley, Calif., 1970), vol. II, 1972, pp. 241-265. MR 413364
  • 3. M. L. Eaton and M. D. Perlman, Reflection groups, generalized Schur functions and the geometry of majorization, Ann. Probab. 5 (1977), 829-860. MR 444864
  • 4. M. L. Eaton, Multivariate probability inequalities: an overview, Tech. Rep. No. 378, Univ. of Minnesota, August 1980.
  • 5. G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, London and New York, 1934.
  • 6. A. Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), 620-630. MR 63336
  • 7. T. Kamae, U. Krengel and G. L. O'Brien, Stochastic inequalities on partially ordered spaces, Ann. Probab. 5 (1977), 899-912. MR 494447
  • 8. A. W. Marshall and I. Olkin, Majorization in multivariate distributions, Ann. Statist. 2 (1974), 1189-1200. MR 362705
  • 9. P. A. Meyer, Probability and potentials, Blaisdell, Waltham, Mass., 1966. MR 205288
  • 10. G. Mudholkar, The integral of an invariant unimodal function over an invariant convex set-an inequality and applications, Proc. Amer. Math. Soc. 17 (1966), 1327-1333. MR 207928
  • 11. I. Schur, Über eine Klasse von Mittelbildungen mit Anwendungen auf die Determinantentheorie, Sitzungsber. Berl. Math. Gesellschaft 22 (1923), 9-20.
  • 12. D. Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463-501. MR 133183

Review Information:

Reviewer: J. H. B. Kemperman
Journal: Bull. Amer. Math. Soc. 5 (1981), 319-324
DOI: https://doi.org/10.1090/S0273-0979-1981-14945-4
American Mathematical Society