Galambos J., Simonelli I. Bonferroni-type Inequalities with Applications

Springer, 1996. — 278 p.This book presents a large variety of extensions of the methods of inclusion and exclusion. Both methods for generating and methods for. The inequalities are utilized for finding asymptotic values ​​and for limit theorems. Applications vary from the classical probability to the modern extreme value theory and combinatorial counting to random subset selection. Applications are given in the prime number theory, growth of digits in different algorithms, and in statistics such as estimates of confidence levels of simultaneous interval estimation. The prerequisites include the basic concepts of probability theory and familiarity with combinatorial arguments.