A very user-friendly book that explains the theory and applications of order statistics. A must have for every Statistician. Well written with tons of references and quite a few examples.

Records when analyzed in terms of sequences of events over time fall into the theory of extreme values. Resnick, Arnold and others have contributed to this theory. This book provides a comprehensive and current account of the theory. There are interesting questions about how long it takes to break a record or how high a record will go. People are particularly interested in this in sports where such records are often kept and publicized. The book is great for researchers and probabilists interested in the mathematical theory. I would have like to see more applications.

The authors have included all mayor topics of the statistical theory of record values and record related statistics up to date. The book constitutes a good text for a graduate-level course on record value theory. However, it is also an essential reference for researchers in the area. Be aware that it is targeted to students and professionals in statistics and scientists requiring statistical analysis (using records). It is not a collection of sensational world record data.

The actual title of this book is "Runs and Scans with Applications". Although patterns does not appear in the title, scans and runs can be viewed as particular patterns of interest in a sequence of binary outcomes. The authors have a good knowledge of both the theory and applications and present both very well without an overload of mathematics. They are also among the major contributors especially contributing articles of an applied nature in reliability and quality assurance testing. They use figures and graphs very effectively.

The runs test of Wald and Wolfowitz goes back to 1940 and is one of the early results in nonparametric statistics. A run of length k is a string of k successive events (often assumed to be independent)where the outcomes are identical (e.g. a run of ten heads in a row). A generalization of this is the occurrence of a scan of type k/m defined as a string of m or fewer outcomes containing k or more events of a particular type (e.g. getting at least 9 heads in a string of 12). A test that a coin is fair could be formulated as a runs or scan test. For a fair coin very long strings of heads or tails would be unusual and observing a long string of say heads might indicate that the coin is weighted to favor heads. Similar tests can be done with scans.

The value of these procedures has been that the distribution theory can be worked out and it can be determined under the null hypothesis what the probabilities are for long runs or how long one can expect to wait for the first run of length k when the null hypothesis is true. This is where the negative binomial distribution comes into the picture.

Many times the authors refer to the works of Sobel and Ebneshahrashoob and also occasionally Uppuluri and Patil. I had the great fortune of knowing and working with the late Ram Uppuluri when I was an employee of the Oak Ridge National Laboratory in the early 1980s. He introduced me to the power of recursion equations in solving problems involving moments of probability distributions and he pointed me toward the powerful tool of the Dirichlet integrals and probability distributions. In fact, Uppuluri along with Sobel and Frankowski published two volumes with tables useful in solving a variety of problems (especially waiting time problems) like the ones discussed in this text through the use of Dirichlet integals. Through Uppuluri, I also met Milton Sobel and later while living in Southern California I met Sobel's student Ebneshahrashoob at Long Beach.

Although their work is discussed in the text, the Dirchlet distribution is not emphasized and the tables are not even referenced. Also the key Chen-Stein ideas are mentioned and referenced but not elaborated on in the book. This I see as a minor shortcoming.

The author do what they set out to do. They introduce the subject in a manner accessible to practitioners and its many applications in a clear and convincing way. They include much of the imprtant literature both recent and historic.

Several books are coming out on this subject these days. It is a hot topic that is being revived because of the recent advances in genetics where scans and runs are useful in gene matching. As an example, check out "Scan Statistics" by Glaz, Naus and Wallenstein. They also have a nice book on this topic and have been major contributors as can be seen from the citations in the Balakrishnan and Koutras book.

I agree completely with the reader from Ithaca. The last time
I used it for something important, there was a serious typo in a
formula, and much time was wasted.

I have mixed feelings about this book.

On the positive side, it contains a wealth of useful information about a large number of continuous probability distribution functions. I use it all the time as a reference in my work. The book contains a extensive bibliography which has been useful time and time again when I need to look up things in the literature.

My first complaint is there are a number of mistakes. I realize this is a huge mass of information and mistakes are inevitable, but I found it quite unacceptable that the probability density function for the Normal distribution was incorrect. Equation 13.1 is missing a factor of sigma in the denominator. This one was quite obvious, but there have been several more subtle errors, which have caused me to waste a large amount of time searching my own work for mathematical errors, until I finally realized the source of the error was the book!

My second complaint is consistency (or lack thereof). The symbols and notation used for one distribution are not necessarily used in the same way for another distribution. This can be quite frustrating! Also, the organization from chapter to chapter (each chapter corresponds to one distribution or one distribution family) is not consistent. For example, for the Lognormal distribution, there is one section (called "Introduction") which gives the pdf of the distribution and a second section (called "Moments and Other Properties") where the moments of the distribution are listed. For the Weibull distribution, both the pdf and the moments are in one section (labeled "Definition"). This sounds like a minor point, until it comes time for you to look one of these things up!

In summary, I need this book to do my job. But I keep wishing there was another book that had the same information, but with better accuracy and organization.

Johnson and Kotz in particular continue their series of ongoing descriptions and analyses of probability/statistics distributions which is an ingenious production. They have the Creative Genius talents of summarizing, organizing, emphasizing open questions, and open mindedness to new ideas (although I have not quite tested them on some very ideas of my own). These qualities in various combinations can also be found in Allday's 1998 book in physics (which I reviewed)and Weinberg's 1974 and later books in physics (some of which I reviewed). Johnson et al. have some Creative Genius categories which are rarely found. For one thing, they cross-categorize distributions ("graphs" for the non-specialist)by their applications to real world problems, which is usually notoriously lacking in math and physics publications (beyond one or two problems). Secondly, they CHARACTERIZE distributions by various properties such as heredity (the same distribution holds for a sum of variables as for one variable, etc.), exponential derivation from other distributions, conditional expectations (I would prefer logic-based probability (LBP) expectations, but it's better than nothing), etc. In other words, their very categorization of distributions is by critical research categories and fundamental logical-factual categories, at least as far as they know them. I recommend this book and the whole series from the same authors (or at least most of them) without reservations except the ones mentioned for LBP, and I urge specialists in these fields to recommend that their students and even "laymen" (non-academic people)purchase this volume and hire a consultant or tutor to translate them or explain them in closer to ordinary English if their probability/statistical background is lacking or deficient.