Book Description
This book is the sixth edition of a classic text that was first published in 1950 in the former Soviet Union. The clear presentation of the subject and extensive applications supported with real data helped establish the book as a standard for the field. To date, it has been published into more that ten languages and has gone through five editions. The sixth edition is a major revision over the fifth. It contains new material and results on the Local Limit Theorem, the Integral Law of Large Numbers, and Characteristic Functions. The new edition retains the feature of developing the subject from intuitive concepts and demonstrating techniques and theory through large numbers of examples. The author has, for the first time, included a brief history of probability and its development. Exercise problems and examples have been revised and new ones added. ... Read more

Customer Reviews (2)

One of the best
I bought my Chesea copy for about 5 bucks while in grad. school, look at it more and more these days. E.g., the derivation of Kolmogorov's 1st pde, the backward time pde for general variable diffusion coefficients, therefore not assuming space or time translational invariance, is hard to find elsewhere in readable form. That equation is important: to within a trivial time transformation it's the (generalized) Black-Scholes pde of 'fair' option pricing in finance. What's lacking is an example of a nontrivial example solved in closed form, one where the transition density g(x,t:x',t') is not symmetric. Let the reader work out the Green function for the drift-free lognormal model for herself in order to see an example that provides insight. In any case, I've looked at Risken and Gardiner and did not find them useful for research. I refer even more often to Stratonovich (Vol. I) and Wax, the classics in the field.

excellent non-measure theoretic treatment of probability
This is a non-measure theoretic treatment of probability whose scope is similar to the first volume of Feller. Although each topic begins witha few simple but insightful examples, what they result is somewhat in-depth discussion. There are minor problems in writing and editing, but I foundnone so serious. This is another amazing Russian mathematics book thatbegins at an elementary level but ends with some real treatment, and thisbook is totally accessible to those who did not rigorously study analysisor measure theory. Highly recommend this to those who seriously desire tostudy probability.

What is also apparent as a feature of this book isthat Gnedenko often notes the details of history. He spends a70-page-appendix for this purpose besides many little footnotes. The authoroften integrates historical evidences as a part of the treatment. I believeone still benefits a lot from this historical notes, even if alreadyfamiliar with the subject.

This book has chapters on the author'sspecialty topics: limit theorems and infinitely divisible distributions.This book also has a chapter on stochastic processes and elements ofstatistics, the latter which Feller's first volume does not touch. However,these brief treatments are only for introductions to each subject. ... Read more

Book Description

Customer Reviews (2)

An illuminating introduction to probability theory.
This brief text, which was written for high school students in the Soviet Union following World War II, is an illuminating introduction to probability theory that does not require a foundation in calculus.The authors develop the theory by generalizing from examples, most of which are taken from military or industrial applications.This gives the reader insight into how mathematicians develop theorems by abstracting from problems arising in the real world.The theorems are proved rigorously except in the final chapter on normal distributions.Formal proofs about normal distributions require advanced mathematics not familiar to the intended audience.

Probability theory is developed in the first section of the text.The authors define probability.They explain the addition rule and how it simplifies when events are mutually exclusive. Likewise, after they obtain the multiplication rule in terms of conditional probabilities, they explain how it simplifies when events are mutually independent.The authors discuss Bayes' formula for the probability of a hypothesis given that a given event has been observed using several examples.They then prove Bernoulli's formula for the most probable number of occurrences of an event when there are a large number of trials.

The second section of the text is on random variables. The authors discuss laws of distribution, mean values, variance and standard of deviation, and how these quantities are used to measure the dispersion of a random variable.Their development culminates in Chebyshev's law of large numbers.In the final chapter on normal distributions, the authors informally discuss their properties and show how they can be used to solve problems.

In a brief conclusion, the authors discuss other developments in probability theory that are beyond the scope of this text.

This text is an excellent introduction to probability theory.I recommend it highly for the insights it offers.However, it does not contain exercises.To learn mathematics, one must solve problems.Therefore, I suggest that you read this text in conjunction with a problem book on probability or a text on probability that does contain exercises such as Samuel Goldberg's Probability: An Introduction.

Old and useful, but get something else
Even though the fifth edition of this book was published in 1961, this book still gives a useful and brief introduction to probability.However, if you're going to buy a book to learn statistics or probability, I would suggest a more recent book.They may not be as brief and concise as this, but newer books would be more up to date.One interesting thing about the Gnedenko/Khinchin book is their examples and problems, which involve things such as the production of artillery shells, or hitting targets with cannons.It is a very welcome change from the traditional, but obvious examples that use decks of cards or dice.Also, it says things about the audience for whom this book was originally meant, and the relevant topics of the time of the cold war.Still, I suggest a more recent text. ... Read more

Book Description
This book provides an introduction to the asymptotic theory of random summation. It describes solving problems in hardware and software reliability, engineering, finance, insurance, computer science, physics and biology. The authors focus on transfer theorems, the classes of limit laws, and convergence of distributions of sums for a number of random variables. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions,and asymptotic behavior of doubly stochastic Poisson processes. ... Read more

Book Description
With the growing complexity of engineered systems, reliability has increased in importance throughout the twentieth century. Initially developed to meet practical needs, reliability theory has become an applied mathematical discipline that permits a priori evaluations of various reliability indices at the design stages. These evaluations help engineers choose an optimal system structure, improve methods of maintenance, and estimate the reliability on the basis of special testing. Probabilistic Reliability Engineering focuses on the creation of mathematical models for solving problems of system design.

Broad and authoritative in its content, Probabilistic Reliability Engineering covers all mathematical models associated with probabilistic methods of reliability analysis, including—unique to this book—maintenance and cost analysis, as well as many new results of probabilistic testing.

To provide readers with all necessary background material, this text incorporates a thorough review of the fundamentals of probability theory and the theory of stochastic processes. It offers clear and detailed treatment of reliability indices, the structure function, load-strength reliability models, distributions with monotone intensity functions, repairable systems, the Markov models, analysis of performance effectiveness, two-pole networks, optimal redundancy, optimal technical diagnosis, and heuristic methods in reliability. Throughout the text, an abundance of real world examples and case studies illustrate and illuminate the theoretical points under consideration.

For engineers in design, operations research, and maintenance, as well as cost analysts and R&D managers, Probabilistic Reliability Engineering offers the most lucid, comprehensive treatment of the subject available anywhere.

About the editor

JAMES A. FALK is Professor and Chairman of the Department of Operations Research at George Washington University. In addition to his numerous publications, Dr. Falk has lectured internationally as a Fulbright Lecturer.

Of related interest...

The reliability-testing "bible" for three generations of Eastern European scientists, adapted for Western scientists and engineers...

HANDBOOK OF RELIABILITY ENGINEERING

Originally published in the USSR, Handbook of Reliability Engineering set the standard for the reliability testing of technical systems for nearly three generations of applied scientists and engineers. Authored by a group of prominent Soviet specialists in reliability, it provides professionals and students with a comprehensive reference covering mathematical formulas and techniques for incorporating reliability into engineering designs and testing procedures. Divided into twenty-four self-contained chapters, the Handbook details reliability fundamentals, examines common reliability problems and solutions, provides a collection of computation formulas, and illustrates practical applications.

The Handbook's Russian editor and internationally recognized expert Igor A. Ushakov has joined with American engineering professionals to bring this indispensable resource to English-speaking engineers and scientists.

1994 (0-471-57173-3) 663 pp. ... Read more

Book Description
Proven statistical reliability analysis methods-available for the first time to engineers in the West While probabilistic methods of system reliability analysis have reached an unparalleled degree of refinement, Russian engineers have concentrated on developing more advanced statistical methods. Over the past several decades, their efforts have yielded highly evolved statistical models that have proven to be especially valuable in the estimation of reliability based upon tests of individual units of systems. Now Statistical Reliability Engineering affords engineers a unique opportunity to learn both the theory behind and applications of those statistical methods. Written by three leading innovators in the field, Statistical Reliability Engineering:
* Covers all mathematical models for statistical reliability analysis, including Bayesian estimation, accelerated testing, and Monte Carlo simulation
* Focuses on the estimation of various measures of system reliability based on the testing of individual units
* Contains new theoretical results available for the first time in print
* Features numerous examples demonstrating practical applications of the theory presented
Statistical Reliability Engineering is an important professional resource for reliability and design engineers, especially those in the telecommunications and electronics industries. It is also an excellent course text for advanced courses in reliability engineering. ... Read more

Customer Reviews (1)

A Deeper Look at Organizational Life
Don't let the title of this fine book scare you off. Hirschhorn's The Workplace Within is one of the finest tools available for the executive who wishes to deepen his or her understanding of what goes on in organizations today. On the other hand, even though it is very clearly written and laden with real-life scenarios from the author's consulting work in organizations, it is not a simple "how to" management text.

Hirschhorn gives very detailed descriptions of what goes wrong in organizations when wedo not question our assumptions. It is almost as if we are sleep walking through our daily work routines, acting out rivalries, making absurd demands on each other, or alternatively, minimzing the actual terror and anxiety we feel.

When read carefully, thoroughly and critically, this book can be a wonderful tool for extending one's social sensitivity in the workplace. It is the kind of book that you can turn to again and again to help illuminate confusing incidents in the workplace and to create attentiveness to one's actual impact on others. As such it is a useful companion to a 360 degree feedback process or participation in an executive assessment or coaching program. ... Read more