Although called “a first course” and structured for use as a course text, this well-presented book on order statistics covers an extensive amount of order statistics theory and practice. This classics edition is a revised edition of the earlier (1992) Wiley-Interscience publication.

The book consists of nine chapters, and ends with a bibliography, author index, and subject index. Each chapter contains an excellent set of exercises that provide varying degrees of challenge to the student; relevant references are included for relatively more difficult problems.

The introductory chapter includes a very useful list of practical situations involving order statistics. The following chapter covers the distributions of order statistics from absolutely continuous populations; the results are illustrated using the uniform and power distributions. Corresponding results for discrete distributions are developed in chapter 3. The specific distributions discussed in the next chapter include Bernoulli, three point, binomial, Poisson, uniform, exponential, logistic, and normal. This chapter concludes with an interesting section on the efficient simulation of clusters of order statistics and single extreme values. Relationships between moments of order statistics, some general and others more specific, are discussed in chapter 5. Chapter 6 looks at the use of order-statistic relationships to characterize functions; this is followed by a detailed discussion on the use of order statistics in estimation and inference for complete and censored samples. Chapter 8 considers the asymptotic distributions of the extremes, as well as of the central and intermediate order statistics. The final chapter deals with the distributions of variously defined order statistics. Some of these results are extended to dependent sequences and improving populations. The connections to nonparametric inference, spacings, censoring, and reliability should have been included.

The book is well organized; the students will find the presentation easy to read. While chapters 1 to 5 and chapter 7 would be of interest to any of the target audiences, selected materials from the remaining chapters can be covered depending on the background of the audience and the time available.

The book is refreshing in many ways, but especially in that it conveys the authors’ love of the subject. Such an intangible quality is as important for the student as an elegant proof. With some exposure to statistics at a reasonable undergraduate level, the text is certainly an excellent starting point for the study of order statistics. This volume is an excellent contribution to the burgeoning flow of fascinating new results concerning ordered statistical data.