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The Theory of Probability
The concept of probability; Sequences of independent trials; Markov chains; Randon variables and distribution functions; Numerical characteristics of Randon variables; The law of large numbers; Characteristic functions; The classical limit theorem; The theory of infinitely divisible distribution laws; The theory of stochastic processes; Elements of queueing theory; Elements of statistics.
Limit Distributions for Sums of Independent Random Variables
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
An Elementary Introduction to the Theory of Probability
This compact volume equips the reader with all the facts and principles essential to a fundamental understanding of the theory of probability. It is an introduction, no more: throughout the book the authors discuss the theory of probability for situations having only a finite number of possibilities, and the mathematics employed is held to the elementary level. But within its purposely restricted range it is extremely thorough, well organized, and absolutely authoritative. It is the only English translation of the latest revised Russian edition; and it is the only current translation on the market that has been checked and approved by Gnedenko himself. After explaining in simple terms the me...
Mathematical Methods of Reliability Theory
Mathematical Methods of Reliability Theory discusses fundamental concepts of probability theory, mathematical statistics, and an exposition of the relationships among the fundamental quantitative characteristics encountered in the theory. The book deals with the set-theoretic approach to reliability theory and the central concepts of set theory to the phenomena. It also presents methods of finding estimates for reliability parameters based on observations and methods of testing reliability hypotheses. Based on mathematical statistics, the book also explains formulation of some selected results. It presents a method that increases the reliability of manufactured articles—redundancy. An impo...
Random Summation
This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the dis...
Statistical Reliability Engineering
Die Zuverlassigkeitsanalyse soll absichern, da? alle Komponenten eines Systems oder Produkts die Anforderungen an Funktionstuchtigkeit, -umfang und Budget erfullen. Alle wichtigen mathematischen Methoden, die in diesem Zusammenhang verwendet werden, stellt in diesem Buch einer der fuhrenden Spezialisten dieses Gebietes vor. Mit vielen realitatsnahen Beispielen und Fallstudien. (05/99)
Probability Theory
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Probabilistic Reliability Engineering
With the growing complexity of engineered systems, reliability hasincreased in importance throughout the twentieth century. Initiallydeveloped to meet practical needs, reliability theory has become anapplied mathematical discipline that permits a priori evaluationsof various reliability indices at the design stages. Theseevaluations help engineers choose an optimal system structure,improve methods of maintenance, and estimate the reliability on thebasis of special testing. Probabilistic Reliability Engineeringfocuses on the creation of mathematical models for solving problemsof system design. Broad and authoritative in its content, Probabilistic ReliabilityEngineering covers all mathematical...
Sums of Independent Random Variables
The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sum...
Applied Reliability Engineering and Risk Analysis
This complete resource on the theory and applications of reliability engineering, probabilistic models and risk analysis consolidates all the latest research, presenting the most up-to-date developments in this field. With comprehensive coverage of the theoretical and practical issues of both classic and modern topics, it also provides a unique commemoration to the centennial of the birth of Boris Gnedenko, one of the most prominent reliability scientists of the twentieth century. Key features include: expert treatment of probabilistic models and statistical inference from leading scientists, researchers and practitioners in their respective reliability fields detailed coverage of multi-stat...
