Bulletin of the American Mathematical Society

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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.

T. W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc. 6 (1955), 170–176. MR 69229, DOI 10.1090/S0002-9939-1955-0069229-1

S. Das Gupta, M. L. Eaton, I. Olkin, M. Perlman, L. J. Savage, and M. Sobel, Inequalitites on the probability content of convex regions for elliptically contoured distributions, Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971) Univ. California Press, Berkeley, Calif., 1972, pp. 241–265. MR 0413364

Morris L. Eaton and Michael D. Perlman, Reflection groups, generalized Schur functions, and the geometry of majorization, Ann. Probability 5 (1977), no. 6, 829–860. MR 444864, DOI 10.1214/aop/1176995655

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.

Alfred Horn, Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), 620–630. MR 63336, DOI 10.2307/2372705

T. Kamae, U. Krengel, and G. L. O’Brien, Stochastic inequalities on partially ordered spaces, Ann. Probability 5 (1977), no. 6, 899–912. MR 494447, DOI 10.1214/aop/1176995659

Albert W. Marshall and Ingram Olkin, Majorization in multivariate distributions, Ann. Statist. 2 (1974), 1189–1200. MR 362705

Paul-A. Meyer, Probability and potentials, Blaisdell Publishing Co. [Ginn and Co.], Waltham, Mass.-Toronto, Ont.-London, 1966. MR 0205288

Govind S. 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, DOI 10.1090/S0002-9939-1966-0207928-6

11.

I. Schur, Über eine Klasse von Mittelbildungen mit Anwendungen auf die Determinantentheorie, Sitzungsber. Berl. Math. Gesellschaft 22 (1923), 9-20.

David Slepian, The one-sided barrier problem for Gaussian noise, Bell System Tech. J. 41 (1962), 463–501. MR 133183, DOI 10.1002/j.1538-7305.1962.tb02419.x

1.

T. W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc. 6 (1955), 170-176. MR 0069229

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