Principles of random variate generation.

*(English)*Zbl 0676.62002
Oxford Science Publications. Oxford: Clarendon Press. xi, 228 p. £35.00 (1988).

This book provides an up-to-date account of the theory and practice of generating random variates from probability distributions. After a brief introduction to simulation, the author discusses the general principles for generating and testing uniform and non-uniform variates. These techniques are applied to different univariate and multivariate distributions, Markov processes and order statistics. Programs written in Fortran 77 for generating the most familiar distributions and a set of graphical aids for the manual generation of variates are included. For the case when competing methods are available, these are compared and their advantages and disadvantages discussed.

Contents: 1. Simulation and random variate generation. 2. Random number sequences. 3. General methods for generating random variates from univariate distributions. 4. Methods of generation from specific continuous distributions. 5. Discrete distributions. 6. Multivariate distributions. 7. Miscellaneous topics. App. 1. FORTRAN 77 routines for generating variates from 15 selected distributions. App. 2. Graphical methods for sampling from standardized gamma distributions (\(\alpha\geq 1)\) and the standardized normal distributions.

Statisticians, operational researchers and computer scientists will find this book to be an accessible and practical introduction to the subject, and it will also be suitable for postgraduate students coming to the subject for the first time.

Contents: 1. Simulation and random variate generation. 2. Random number sequences. 3. General methods for generating random variates from univariate distributions. 4. Methods of generation from specific continuous distributions. 5. Discrete distributions. 6. Multivariate distributions. 7. Miscellaneous topics. App. 1. FORTRAN 77 routines for generating variates from 15 selected distributions. App. 2. Graphical methods for sampling from standardized gamma distributions (\(\alpha\geq 1)\) and the standardized normal distributions.

Statisticians, operational researchers and computer scientists will find this book to be an accessible and practical introduction to the subject, and it will also be suitable for postgraduate students coming to the subject for the first time.

Reviewer: J.Antoch

##### MSC:

62-02 | Research exposition (monographs, survey articles) pertaining to statistics |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65C10 | Random number generation in numerical analysis |

62-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics |

62-04 | Software, source code, etc. for problems pertaining to statistics |

65C05 | Monte Carlo methods |

65-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to numerical analysis |

65-04 | Software, source code, etc. for problems pertaining to numerical analysis |