- 原书名：Probability Inequalities
- 原出版社： Springer
Inequality has become an essential tool in many areas of mathematical research, for example in probability and statistics where it is frequently used in the proofs. Probability Inequalities covers inequalities related with events, distribution functions, characteristic functions, moments and random variables (elements) and their sum. The book shall serve as a useful tool and reference for scientists in the areas of probability and statistics, and applied mathematics.
Prof. Zhidong Bai is a fellow of TWAS and the Institute of Mathematical Statistics; he is a professor at the National University of Singapore and Northeast Normal University, Changchun, China.
1.1 Inclusion-exclusion Formula
1.2 Corollaries of the Inclusion-exclusion Formula
1.3 Further Consequences of the Inclusion-exclusion Formula
1.4 Inequalities Related to Symmetric Difference
1.5 Inequalities Related to Independent Events
1.6 Lower Bound for Union (Chung-ErdSs)
Chapter 2 Inequalities Related to Commonly Used Distributions
2.1 Inequalities Related to the Normal d.f.
2.2 Slepian Type Inequalities
2.3 Anderson Type Inequalities
2.4 Khatri-Sidak Type Inequalities
2.5 Corner Probability of Normal Vector
2.6 Normal Approximations of Binomial and Poisson Distributions
Chapter 3 Inequalities Related to Characteristic Functions
3.1 Inequalities Related Only with c.f
3.2 Inequalities Related to c.f. and d.f.
3.3 Normality Approximations of c.f. of Independent Sums