Albert W. Marshall, Professor Emeritus of Statistics at the University of British Colombia, previously served on the faculty of the University of Rochester and on the staff of the Boeing Scientific Research Laboratories. His fundamental contributions to reliability theory have had a profound effect in furthering its development.

Ingram Olkin is Professor Emeritus of Statistics and Education at Stanford University, after having served on the faculties of Michigan State University and the University of Minnesota. He has made significant contributions in multivariate analysis and in the development of statistical methods in meta-analysis, which has resulted in its use in many applications.

Professors Marshall and Olkin, coauthors of papers on inequalities, multivariate distributions, and matrix analysis, are about to celebrate 50 years of collaborations. Their basic book on majorization has promoted awareness of the subject, and led to new applications in such fields as economics, combinatorics, statistics, probability, matrix theory, chemistry, and political science.

The second edition of this classic reference oo inequalities offers an
ever broader survey of this area fundemental to many areas of
statistics and mathematics.

Introduction.- Doubly Stochastic Matrices.- Schur-Convex Functions.- Equivalent Conditions for Majorization.- Preservation and Generation of Majorization.- Rearrangements and Majorization.- Combinatorial Analysis.- Geometric Inequalities.- Matrix Theory.- Numerical Analysis.- Stochastic Majorizations.- Probabilistic, Statistical, and Other Applications.- Additional Statistical Applications.- Orderings Extending Majorization.- Multivariate Majorization.- Convex Functions and Some Classical Inequalities.- Stochastic Ordering.- Total
Positivity.- Matrix Factorizations, Compounds, Direct Products, and M-Matrices.- Extremal Representations of Matrix Functions.