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Random number generation and Monte Carlo methods. (English) Zbl 0972.65003

Statistics and Computing (Cham). New York, NY: Springer. xiv, 247 p. (1998).
This is a textbook on random number generation and basic Monte Carlo methods. It contains the description of basic random number generators, transformation of uniform deviates (general and specific for more common 20 distributions), generation of random samples and permutations, basic Monte Carlo methods, testing of random number generation, software for random numbers, and Monte Carlo methods in statistics.
The book contains an excessive bibliography (almost 40 pages) including WWW links and journals. Each chapter contains excercises.
The book presents mainly the principles of random number generation algorithms. It requires no deeper knowledge of mathematical statistics. It is paid by the lack of a deeper explanation of some more subtle problems.
The book is a quite good introduction into the problems of random number generation and Monte Carlo methods for software oriented people. The author of such a book must always omit some topics. It is a matter of taste which ones. Nevertheless it seems that some more space should have been devoted to the testing of the generators [missing tests based on Monte Carlo simulation, only one test set is presented, missing metatest from e.g. D. A. Dahl, C. L. Atwood and R. A. LaVioletta, Appl. Math. Modelling 24, No. 10, 771-778 (2000; Zbl 0972.65002) or J. Král, Inf. Process. Lett. 1, 164-167 (1972; Zbl 0236.65007)].
It is known from both the above mentioned papers that the random shuffling technique can be generalized with very good results even for additive generators working with very short arithmetics. This fact is not mentioned.
It would be good to give more hints what existing generators are according to practical experience reliable.

MSC:

65C10 Random number generation in numerical analysis
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
11K45 Pseudo-random numbers; Monte Carlo methods
65C05 Monte Carlo methods
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