This book presents a large variety of extensions of the methods of inclusion and exclusion. Both methods for generating and methods for proof of such inequalities are discussed. The inequalities are utilized for finding asymptotic values and for limit theorems. Applications vary from classical probability estimates to modern extreme value theory and combinatorial counting to random subset selection. Applications are given in 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.

Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and number theory. It uses entirely probabilistic arguments in actualizing the potential of the asymptotic theory of products of independent random variables and obtaining results with dependent variables using a new Bonferroni-type argument. Systematically and comprehensively tracks the progression of research completed in the area over the last twenty years. Well-indexed and well-referenced, Products of Random Variables -Clarifies foundational concepts such as symmetric and limiting distributions of products -Examines various limit theorems, from logarithmically Poisson distributions to triangular arrays -Explores characterization theorems, detailing normal, Cauchy, and bivariate distributions -Describes models of interactive particles -Elucidates dual systems of interactive particles, dual systems of increasing size, and random walks -Covers the Kubilius-Turan inequality and distributions for multiplicative functions -Probes sequences of prime divisors and prime numbers -Discusses Markov chains, Hilbert spaces, and quotients of random variables -Presents income growth models and numerous other applied models tapping products of random variables Authored by eminent scholars in the field, this volume is an important research reference for applied mathematicians, statisticians, physicists, and graduate students in these disciplines.