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Elements of simulation
Book Reoiews
251
Byron J.T. M O R G A N
A. Bruce CLARKE and Ralph L. DISNEY
Elements of Simulation
Probability and Random Processes: A Fir~t Course with Applications
Chapman an.d Hall, London, 1984, xiii+ 351 pages, £12.95 This is a very readable book in which the basic tools of simulation are excellently explained and nicely illustrated with interesting examples. What is meant by "basic tools" is best illustrated by describing the contents. After an introductory chapter, in chapter 2 (39 pages) the necessary statistical knowledge is reviewed; the standard is Clarke and Cooke (1983). The chapters 3-6 (109 pages) deal with generating uniform and non-uniform random variables, and testing random numbers. In chapter 7 (30 pages) variance-reduction techniques are discussed and applied to the evaluation of one-dimensional integrals and the M / M / 1 queue. In the last two chapters (46 pages) practical examples are given of the use of simulation. In chapter 8 the discussion concentrates on the problems that arise when applying simulation, while in chapter 9 the kaleidoscopic effect of the applications is more important. Finally there are two appendices; in the first one a number of useful algorithms are mentioned which are available in the NAG and IMSL libra ies, and in the second one tables of pseudorandom digits, normal and exponential variates are given. The 232 exercises, taking up 58 pages and another 43 pages for the solutions are an essential part of the book, and many of them ought to be discussed in any simulation course. Throughout the t*.xt many BASIC programs illustrate how the algorithms can be translated in computer programs. V I had to add a critical remark, I would say that a more detc.iled discussion of the bootstrap technique would have fitted excellently in the overall approach. But I shall not do that, it is just a pleasure to recommend the book to a wide audience of students as well as teachers. P.C. S A N D E R Eindhoven University of Technology Eindhoven, Netherlands Reference
Clarke, G.M., zuadCooke, D. (1983), .4 Basic Course in Statistics I2nd Edn.), Arnold, London.
Second edition, Wiley, New York, 1985, xii + 324 pages, £32.95 This is the second edition of a book previously published :~n 1970 with the title Probability and Random P:rocesses for Engineers and Scientists. It is an introductory book for undergraduates and presents e.lementary probability and stochastic processes in a fairly formal mathematical style. The first seven chapters cover the usual material for a first course in probability: probabilities of events, discrete and continuous random var.iablex, joint distributions, expectation and moments, special distributions, taws of large numbers and the central limit theorem. There follows a very brief discussion of some statistics: testing for indeper~dence using contingency tables, estimation v~- th,~. method of moments, the X2 goodness-of-fit te.,;t and the Kolmogorov-Smirnov test. The remaining five chapters are ttlen used to introduce discrete and continuous parameter Markov chains and some simple queueing theory. Here some results (for example, those for the classification of states and limiting distributions of Markov chains) are quoted without proof. Throughout the book the chosen material is carefully motivated and very clearly explained, the presentation being most suitable for those with a mathematical background. There are plenty of e~;amples and exercises and many of these involve real applications, although there are also many of the conventional coin or dice variety. For those familiar with the first edition, the main changes in the new edition are the addition of chapters on functions of random variabt,es and on fitting distributions to data (outlined above) and the removal of material on matrix algebra in connection with Markov chains, on non-irreducible Markov chair, s and on the Weiner process. One minor complaint is that examples are headed by the werd EXAMPLEin apper case bold print together with a line going right across the page. Section headings on the other hand are in lower case print (with no line) and are much less conspicuous. Thus the text appears dominated by the examples, even though these may oni- be a few lines long, especially since it is often not obvious
251
Byron J.T. M O R G A N
A. Bruce CLARKE and Ralph L. DISNEY
Elements of Simulation
Probability and Random Processes: A Fir~t Course with Applications
Chapman an.d Hall, London, 1984, xiii+ 351 pages, £12.95 This is a very readable book in which the basic tools of simulation are excellently explained and nicely illustrated with interesting examples. What is meant by "basic tools" is best illustrated by describing the contents. After an introductory chapter, in chapter 2 (39 pages) the necessary statistical knowledge is reviewed; the standard is Clarke and Cooke (1983). The chapters 3-6 (109 pages) deal with generating uniform and non-uniform random variables, and testing random numbers. In chapter 7 (30 pages) variance-reduction techniques are discussed and applied to the evaluation of one-dimensional integrals and the M / M / 1 queue. In the last two chapters (46 pages) practical examples are given of the use of simulation. In chapter 8 the discussion concentrates on the problems that arise when applying simulation, while in chapter 9 the kaleidoscopic effect of the applications is more important. Finally there are two appendices; in the first one a number of useful algorithms are mentioned which are available in the NAG and IMSL libra ies, and in the second one tables of pseudorandom digits, normal and exponential variates are given. The 232 exercises, taking up 58 pages and another 43 pages for the solutions are an essential part of the book, and many of them ought to be discussed in any simulation course. Throughout the t*.xt many BASIC programs illustrate how the algorithms can be translated in computer programs. V I had to add a critical remark, I would say that a more detc.iled discussion of the bootstrap technique would have fitted excellently in the overall approach. But I shall not do that, it is just a pleasure to recommend the book to a wide audience of students as well as teachers. P.C. S A N D E R Eindhoven University of Technology Eindhoven, Netherlands Reference
Clarke, G.M., zuadCooke, D. (1983), .4 Basic Course in Statistics I2nd Edn.), Arnold, London.
Second edition, Wiley, New York, 1985, xii + 324 pages, £32.95 This is the second edition of a book previously published :~n 1970 with the title Probability and Random P:rocesses for Engineers and Scientists. It is an introductory book for undergraduates and presents e.lementary probability and stochastic processes in a fairly formal mathematical style. The first seven chapters cover the usual material for a first course in probability: probabilities of events, discrete and continuous random var.iablex, joint distributions, expectation and moments, special distributions, taws of large numbers and the central limit theorem. There follows a very brief discussion of some statistics: testing for indeper~dence using contingency tables, estimation v~- th,~. method of moments, the X2 goodness-of-fit te.,;t and the Kolmogorov-Smirnov test. The remaining five chapters are ttlen used to introduce discrete and continuous parameter Markov chains and some simple queueing theory. Here some results (for example, those for the classification of states and limiting distributions of Markov chains) are quoted without proof. Throughout the book the chosen material is carefully motivated and very clearly explained, the presentation being most suitable for those with a mathematical background. There are plenty of e~;amples and exercises and many of these involve real applications, although there are also many of the conventional coin or dice variety. For those familiar with the first edition, the main changes in the new edition are the addition of chapters on functions of random variabt,es and on fitting distributions to data (outlined above) and the removal of material on matrix algebra in connection with Markov chains, on non-irreducible Markov chair, s and on the Weiner process. One minor complaint is that examples are headed by the werd EXAMPLEin apper case bold print together with a line going right across the page. Section headings on the other hand are in lower case print (with no line) and are much less conspicuous. Thus the text appears dominated by the examples, even though these may oni- be a few lines long, especially since it is often not obvious