Statistical Distributions

Rating:
Summary: Great resource for Statisticians and Quantitative analysts.
Review: I have been browsing in bookstores for months looking for something just like this. It has very detailed descriptions and explanations of important elements, such as mean, variance, moment-generating functions, etc. I was a bit dismayed by the price, but more than happy with the information it provided.

Rating:
Summary: Very helpful
Review: No book can possibly cover all distributions - new ones seem to show up in every new problem that arises. This book covers the common ones, maybe all the distributions a student sees in the first stats course or two.

The coverage is quite good for routine, and some non-routine purposes. I find the characteristic functions especially helpful. Each distribution's description of how it arises is also very useful - it's the kind of information that a practitioner needs in order to apply distributions to problems in meaningful ways.

I know that no book can say everything, but a few additions would have improved this book significantly. More discussion of applications would have helped. So would a discussion of general techniques for generating random numbers - inverse distributions, rejection, etc.

The two real weaknesses I found were in the extreme value and the empirical distributions. Extreme values don't stand alone. They often arise in ways dependent on other distributions. An extreme value distribution might describe the results of many experiments that find the largest of N values drawn from distribution P - with different results according to P. These distributions don't have convenient closed forms, but are amenable to some kinds of analysis anyway.

Perhaps the authors do a reasonable job of empirical distributions in the continuous case, but discrete (categorical) cases arise more in my work. Discrete distributions must answer such questions as: given that my sampling may not have found objects of all possible types, how many unknown types are probably still out there? Lots of problems have distributions too complicated for analysis or too poorly understood for book formulas to work, and must be handled empirically. More discussion of empirical techniques would make this a much stronger reference.

Despite its soft spots, this is a very practical reference. I expect it to be a productive member of my technical library.

Rating:
Summary: Great overview - missing Levy flights; no index
Review: This is a very good overview of a variety of statistical distributions. I particularly like the empirical distribution, which gives a detailed method for constructing a distribution from empirical data.

However, it lacks some details that I am interested in such as the Levy distribution, robust comparisons between empirical and theoretical distributions, and a focus or discussion on distribution tails.

I knocked off another star because, incredibly, the book lacks and index.

Rating:
Summary: the only book you'll ever need on distributions
Review: This is a very good reference for univariate statistical distributions. It provides maximum likelihood and moment estimation formulas for many distributions i'ven't seen anywhere else. That's right that the price is quite high for the number of pages but this information is invaluable for practitioners who need to fit distributions to real data.

Rating:
Summary: Want to fit distributions ? This is the book !
Review: This is a very good reference for univariate statistical distributions. It provides maximum likelihood and moment estimation formulas for many distributions i'ven't seen anywhere else. That's right that the price is quite high for the number of pages but this information is invaluable for practitioners who need to fit distributions to real data.

Rating:
Summary: concise handbook
Review: This is an extremely valuable compendium of what almost any pracitioner needs to know about 40 of the most commonly used statistical distributions. It is designed as a quick lookup reference for each of the distributions. Most chapters begin with a few brief lines describing some of the applications of the distribution, and then provide a list of relevant formulae, such as for the distribution function, probability density, moments etc. Relationships to other distributions are defined, means of estimating the parameters provided, and ways of generating random numbers from the distribution are indicated.
Graphs of the distributions are shown with varying parameter values in most cases.

The book should be seen purely as a handbook on statistical distributions, not as a theoretical reference. The book is ideal for those who make use of statistical distributions in other fields, and who are not necessarily statisticians themselves. I have no formal statistics training, but use distributions extensively in my own work, and found this book very easy to understand. I have been using Johnson and Kotz monographs fairly extensively as references for the distributions in which I am interested, but find this book a much simpler reference for the basic facts of the distributions. In addition, its consistent use of notation across the chapters makes it much easier for the reader to cross reference.

I refrain from giving 5 stars to the book because of a few weaknesses, primarily omissions. Firstly, as an earlier reviewer pointed out, the lack of an index is a little annoying sometimes. Secondly, the bibliography is very slim, and so the reader interested in finding further details, proofs etc., is given very little direction. Thirdly, there are a few obvious omissions, such as the cumulative distribution function for the chi-squared distribution. Fourthly, random number generation is described only when the generation is relatively simple (for example, a method for generating random variates from a gamma distribution is described only for special cases). Finally, I would like to have seen more guidance provided in the sections on parameter estimation, such as first and second derivatives of log-likelihood functions when the estimates have to be derived iteratively.

Rating:
Summary: the only book you'll ever need on distributions
Review: This is the most thorough reference on distributions that I have found. The information contained about each distribution is concisely stated in a few pages - you would probably have to look in several books to get the same material. Most useful to people writing digital simulations is instructions on how to generate the distribution using random number generators. This is especially useful if you don't have access to statistical software packages. Lack of an index detracts, but is minor. Listings are alphabetical, by distribution name, so you might have to page through the book to find one that is not in an obvious location (like continuous uniform is listed as "rectangular", but discrete uniform is listed as "discrete uniform"). You need to be familiar with basic statistics to understand the book; but you don't have to be a statistician.