Probability Inequalities in Multivariate Distributions

✍ Scribed by Y. L. Tong

• Publisher: Academic Press
• Year: 1980
• Tongue: English
• Leaves: 247
• Series: Probability and mathematical statistics
• Category: Library

✦ Synopsis

Probability Inequalities in Multivariate Distributions is a comprehensive treatment of probability inequalities in multivariate distributions, balancing the treatment between theory and applications. The book is concerned only with those inequalities that are of types T1-T5. The conditions for such inequalities range from very specific to very general.

Comprised of eight chapters, this volume begins by presenting a classification of probability inequalities, followed by a discussion on inequalities for multivariate normal distribution as well as their dependence on correlation coefficients. The reader is then introduced to inequalities for other well-known distributions, including the multivariate distributions of t, chi-square, and F; inequalities for a class of symmetric unimodal distributions and for a certain class of random variables that are positively dependent by association or by mixture; and inequalities obtainable through the mathematical tool of majorization and weak majorization. The book also describes some distribution-free inequalities before concluding with an overview of their applications in simultaneous confidence regions, hypothesis testing, multiple decision problems, and reliability and life testing.

This monograph is intended for mathematicians, statisticians, students, and those who are primarily interested in inequalities.

✦ Table of Contents

Content:
Front Matter, Page iii
Copyright, Page iv
Preface, Pages ix-x
Acknowledgments, Pages xi-xii
Notation, Page xiii
CHAPTER 1 - Introduction, Pages 1-6
CHAPTER 2 - Inequalities for Multivariate Normal Distribution, Pages 7-35
CHAPTER 3 - Inequalities for Other Well-known Distributions, Pages 36-49
CHAPTER 4 - Integral Inequalities Over A Symmetric Convex Set, Pages 50-76
CHAPTER 5 - Inequalities via Dependence, Association, and Mixture, Pages 77-101
CHAPTER 6 - Inequalities Via Majorization and Weak Majorization, Pages 102-141
CHAPTER 7 - Distribution-Free Inequalities, Pages 142-163
CHAPTER 8 - Some Applications, Pages 164-207
Bibliography, Pages 208-231
Author Index, Pages 233-235
Subject Index, Pages 236-239
Probability and Mathematical Statistics: A Series of Monographs and Textbooks, Pages ibc1-ibc2