The series of books are must for every statistician, period.

This book was providencial during my Master in Statistics research. It is THE reference when it comes to discrete distributions, a topic in Stats which has bloomed in the last two decades. This new edition covers some state-of-the-art topics in the field, such as mixture distributions and new families of discrete random variables. It is well written, but never verbose: it cuts to the chase and will be of great help to a practitioner in dire need of an arcane test. And finally, believe it or not, discrete random variables are FUN. The more you know about them, the more you perceive they can be applied in almost any practical situation. And you don't need much more than the contents of this book to be an expert.

The quality movement in the US in the 1980s and 1990s has led to a great deal of quality efforts that stress statistical measurements of process capability. These indices are intended to answer the question "How often will a manufactured part fall outsided specification limits?" Certain standards and tests based on capability indices have validity when the process variation has a normal distribution.

However, it has been my experience in the medical device industry that many processes are non-normal and that the application of the normal theory in these cases can lead one astray. Others have found this to be the case in the automobile industry as well as in other industries.

Also some people treat these indices as though they are known constants when in practice we almost always use sample estimates of means and standard deviations in our calculation of the index. This means that the "index" is itself an estimate of the capability parameter.

These issues are recognized and emphasized by Kotz and Johnson in this wonderful little monograph. It was the first book to address many of these issues and to summarize what it known based on the scattered literature. They treat all the major indices and present normal theory and bootstrap alternatives among others. It is very authoritative and is an important reference for anyone dealing with these quality control issues.

The objectives of this text are very similar to the objectives in the Kotz and Johnson treatise of 1993. Written 5 years later this text can be looked at in part as an update to that volume.

However, that book was more of a reference manual for process capability whereas this book reads more like a course text including many more illustrations and examples. Also there is an attempt here to include both the theoretical and applied aspects of capability indices.

It covers the available distribution theory results for processes with normal distributions and non-normal as well. The effect of non-normality is carefully analyzed and alternative methods including the bootstrap are considered. This has all the attributes of Kotz and Johnson book but is more current, more detailed and has more references.

This book is a broad survey of both univariate and multivariate extreme value distributions. The target reader is someone who wants quick access to results so the book has no proofs, although there are motivating theoretical discussions in the first chapter. This book has considerable overlap with a chapter in Kotz's book: Continuous Univariate Distributions, Vol. 2. The book is thin (too thin for such a vast subject) with only three chapters. There are no worked problems or sample data sets, so the person wanting a tutorial work should look elsewhere. This book is primarily a reference work, not a text, or a monograph. Unfortunately, there are a number of annoying errors and omissions. For example, on page 23 (section 1.7.1 Moment Estimation) the moment equations for sigma and mu reversed. In chapter 2, which covers generalized extreme value distributions, the authors reference Castillo and Hadi (1997), but this reference is missing from the bibliography. Too bad, as this is an essential reference for the chapter because as it gives a good method for estimating the parameters of a generalized extreme value distribution. Although there is a section on Bayesian inference, try looking up "Bayes" or "Bayesian" in the index-- nothing. The index is entirely inadequate, especially for a reference work. If I had paid for this book with my own money, I would have returned it.

The statistics of extremes has a variety of applications including: civil engineering, reliability, meteorology, seismology, hydrology, insurance, and finance, to name but a few. The classic reference has been the book by Gumbel-- a tour-de-force of the subject. However, that book predates modern developments in numerical methods so it is dated. Castillo (1988) updates Gumbel with a number of results that don't even appear in the Kotz book.

I wish I could recommend "Extreme Value Distributions" because of the many fine other books authored by Kotz, but I can't. Unfortunately, it looks like it was put together in a hurry, the reader deserves better.

The theory of extremes and related topics of outlier detection are near and dear to me. My Ph.D. thesis dealt with special stationary sequences and how Gnedenko's three type theorem extended from the i.i.d. case to stationary sequences. Also after getting my Ph.D. I went to Oak Ridge National Laboratory where I continued to do research on extremes and focused on the problem of outlier detection and its relation to data validation.

There have been a number of theoretical books on the theory of extremes. Gumbel's was the first and it was also considered very practical. Galambos and Leadbetter,Lindgren and Rootzen are the landmark theoretical books that extend the theory. Castillo wrote a book for engineers and in recent years there have been additional books of a theoretical nature but with applications to finance or hydrology etc.

This book is a reference for engineers and others that may want to use the distributions and apply the methods. It is also useful to the extreme value theorists like myself.

Kotz has always been known for his ability to characterize and provide historical accounts for probability distributions. His volumes with Norman Johnson are famous. This book is up to his high standards. Chapter 1 provides a thorough and accurate historical account of the development of the theory of univariate extremes. Chapter 2 provides information on the family of generalized extreme value distributions. Finally Chapter 3 covers the theory and distributions for multivariate extremes along with applications. This is followed by a large and extensive bibliography. Although my own work is not mentioned directly in this book it can be found in some of the references including Castillo (1988) and Leadbetter, Lindgren and Rootzen (1983).

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.