Probability Inequalities

• Main Authors: Lin, Zhengyan (Author), Bai, Zhidong (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Subjects: Mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.

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...

Table of Contents:

• Elementary Inequalities of Probabilities of Events
• Inequalities Related to Commonly Used Distributions
• Inequalities Related to Characteristic Functions
• Estimates of the Difference of Two Distribution Functions
• Probability Inequalities of Random Variables
• Bounds of Probabilities in Terms of Moments
• Exponential Type Estimates of Probabilities
• Moment Inequalities Related to One or Two Variables
• Moment Estimates of (Maximum of) Sums of Random Variables
• Inequalities Related to Mixing Sequences
• Inequalities Related to Associative Variables
• Inequalities about Stochastic Processes and Banach Space Valued Random Variables.