Inequalities: Theory of Majorization and Its Applications

The theory of inequalities has applications in virtually every branch of mathematics. This revised and expanded edition of a classic work on inequalities will be of interest to statisticians, probabilists, and mathematicians.

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.

From the reviews of the second edition: The second edition of the praised classic without whom I know that some people never leave home . attempts to bring these uses to the fore so that the reader can see the extent and variation in its use. The chapters of the original version remain intact . The bibliography has increased by over 50%. Needless to say, the revised volume obviously continues as a celebrated classic. (Simo Puntanen, International Statistical Review, Vol. 79 (2), 2011)

Autorentext

Albert W. Marshall is Professor Emeritus of Statistics at the University of British Columbia. His fundamental contributions to reliability theory have had a profound effect in furthering its development. Ingram Olkin is Professor Emeritus of Statistics at Stanford University. He has made fundamental contributions in multivariate analysis, and in the development of statistical methods in meta-analysis, which have resulted in its use in many applications. Barry C. Arnold is Distinguished Professor of Statistics at the University of California, Riverside. His previous books deal with Pareto Distributions, Order Statistics, Record Values, Conditionally Specified Distributions, and the Lorenz Order.

Zusammenfassung
This greatly expanded new edition includes recent research on stochastic, multivariate and group majorization, Lorenz order, and applications in physics and chemistry, in economics and political science, in matrix inequalities, and in probability and statistics.

Inhalt
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.