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.