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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.
This work thoroughly covers the concepts and main results of
probability theory, from its fundamental principles to advanced
applications. This edition provides examples early in the text of
practical problems such as the safety of a piece of engineering
equipment or the inevitability of wrong conclusions in seemingly
accurate medical tests for AIDS and cancer.;College or university
bookstores may order five or more copies at a special student price
which is available upon request from Marcel Dekker, Inc.
This work thoroughly covers the concepts and main results of
probability theory, from its fundamental principles to advanced
applications. This edition provides examples early in the text of
practical problems such as the safety of a piece of engineering
equipment or the inevitability of wrong conclusions in seemingly
accurate medical tests for AIDS and cancer.;College or university
bookstores may order five or more copies at a special student price
which is available upon request from Marcel Dekker, Inc.
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.
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