##
**Multivariate statistical simulation.**
*(English)*
Zbl 0604.62056

Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. New York etc.: John Wiley & Sons. IX, 230 p. £33.75 (1987).

This book was primarily written for the researcher who is confronted with the task of designing and executing a simulation study that will employ continuous multivariate distributions.

The book is divided into eleven chapters. Chapter 1 has an introductory character: robustness of \(T^ 2\), error rates in partial discriminant analysis, Foutz’ goodness-of-fit test, and an overview of the subsequent chapters. Chapter 2 provides a discussion of the univariate distributions and their generation needed in the sequel. Some multivariate generation preliminaries are provided in Chapter 3. Chapters 4 through 10 deal with specific multivariate distributions: multivariate normal and related distributions; Johnson’s translation system; elliptically contoured distributions; circular, spherical, and related distributions, Khintchine distributions, multivariate Burr, Pareto, and logistic distributions; miscellaneous distributions that have occasionally been used in simulation work: the Morgenstern, Plackett, Gumbel, and Ali-Mikhail-Haq. Further potentially fruitful research directions are briefly sketched in Chapter 11.

The book includes a large number of references. Written in a lively, engaging style, this book will prove invaluable to all those who are concerned with simulation. Although not designed as a text, it can also be used for a one-semester graduate course in simulation.

The book is divided into eleven chapters. Chapter 1 has an introductory character: robustness of \(T^ 2\), error rates in partial discriminant analysis, Foutz’ goodness-of-fit test, and an overview of the subsequent chapters. Chapter 2 provides a discussion of the univariate distributions and their generation needed in the sequel. Some multivariate generation preliminaries are provided in Chapter 3. Chapters 4 through 10 deal with specific multivariate distributions: multivariate normal and related distributions; Johnson’s translation system; elliptically contoured distributions; circular, spherical, and related distributions, Khintchine distributions, multivariate Burr, Pareto, and logistic distributions; miscellaneous distributions that have occasionally been used in simulation work: the Morgenstern, Plackett, Gumbel, and Ali-Mikhail-Haq. Further potentially fruitful research directions are briefly sketched in Chapter 11.

The book includes a large number of references. Written in a lively, engaging style, this book will prove invaluable to all those who are concerned with simulation. Although not designed as a text, it can also be used for a one-semester graduate course in simulation.

Reviewer: R.Theodorescu

### MSC:

62H99 | Multivariate analysis |

65C99 | Probabilistic methods, stochastic differential equations |

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

65C10 | Random number generation in numerical analysis |