Inequalities: Theory of Majorization and Its Applications

1. Introduction
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

2. Doubly Stochastic Matrices
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

3. Schur-Convex Functions
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

4. Equivalent Conditions for Majorization
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

5. Preservation and Generation of Majorization
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

6. Rearrangements and Majorization
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

7. Combinatorial Analysis
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

8. Geometric Inequalities
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

9. Matrix Theory
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

10. Numerical Analysis
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

11. Stochastic Majorizations
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

12. Probabilistic, Statistical, and Other Applications
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

13. Additional Statistical Applications
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

14. Orderings Extending Majorization
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

15. Multivariate Majorization
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

16. Convex Functions and Some Classical Inequalities
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

17. Stochastic Ordering
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

18. Total Positivity
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

19. Matrix Factorizations, Compounds, Direct Products, and M-Matrices
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

20. Extremal Representations of Matrix Functions
Albert W. Marshall, Ingram Olkin, Barry C. Arnold

Keywords: Statistics, Statistical Theory and Methods