Continuous multivariate distributions. Vol. 1: Models and applications. 2nd ed.

*(English)*Zbl 0946.62001
New York, NY: Wiley. xxii, 722 p. (2000).

The first edition of Continuous Multivariate Distributions (CMD) was published in 1972 as the fourth and final volume of the series “Distributions in Statistics”, see the review Zbl 0248.62021. Now, this volume is split into two parts, the first is on models and applications. Besides this split the size raised from 333 to 722 pages. This shows the incredible increase of material published during the last three decades. It contains eleven chapters, numbered from 44 to 55 in continuation of the chapter numbers in the first four volumes of the new series: Systems of CMD, M Normal D, Bivariate and Trivariate Normal D, M Exponential D, M Gamma D, Dirichlet and Inverted Dirichlet D, M Liouville D, M Logistic D, M Pareto D, Bivariate and M Extreme Value D, Natural Exponential Families. The sizes of the chapters vary considerably. The largest are on the distributions related to the normal d. and the exponential d. (90 to 140 pages); the shortest chapter is on the Liouville d. (21 pages).

Not included are the Wishard and the multivariate t-distributions and other sampling distributions associated with the normal d. Perhaps, they will be the core of volume 2 of CMD, which will be the final volume of the new series.

Thanks to the development of computing power and programs it was possible to reduce the references to published tables. More ambitious practical applications are described instead. The about 1400 references lead the interested reader to the sources and to further material.

This book contributes well to the purpose of the series to give an in-depth account of the statistical distributions. For certain it will serve as the primary source for continuous multivariate statistical distributions for a long time.

Not included are the Wishard and the multivariate t-distributions and other sampling distributions associated with the normal d. Perhaps, they will be the core of volume 2 of CMD, which will be the final volume of the new series.

Thanks to the development of computing power and programs it was possible to reduce the references to published tables. More ambitious practical applications are described instead. The about 1400 references lead the interested reader to the sources and to further material.

This book contributes well to the purpose of the series to give an in-depth account of the statistical distributions. For certain it will serve as the primary source for continuous multivariate statistical distributions for a long time.

Reviewer: R.Schlittgen (Hamburg)

##### MSC:

62-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to statistics |

62H10 | Multivariate distribution of statistics |