This book covers various properties of the normal and Student probability distributions. After an introduction, there is a chapter on each of these. A chapter on sums, products and differences of normal distributions is followed by a similar chapter on such combinations of Student distributions. Then there are two chapters on combining a normal with a Student. Two final chapters deal with various ways of characterizing the two distributions that are the subject of this book. Thus the book is perhaps more narrow than the title might suggest. Despite the title, very few applications are mentioned. There are a number of useful graphs in color but low resolution.
The general format is to refer the reader to other works for details and prove only some of the key results. There is a long bibliography and the references to it are quite specific. For example, one might be sent to three papers for applications of a result. On the whole this seems a very useful reference for a very narrow audience.
Unfortunately, the book contains a huge number of typos and formating problems. The spine says “Atlantis Press,” which is an imprint of Springer. A brief description inside sheds no light on why the volume does not appear to have been proofread. A frequent problem is that the article “the” is often missing where needed for idiomatic English. In the twenty-first century, statistics is a very international discipline, and experienced editors should be aware that this problem is very common among authors whose native language is not English.
An even more pervasive problem is chaotic use of italics. The usual convention is to put algebraic variables in italics. Sometimes the authors are consistent about this, but often not. Early in the book they seem to italicize variables in displayed equations but not in paragraph text. Later this convention seems to have been abandoned. At times variables wander in and out of italics within the statement of a single theorem. Usually one can figure out what is meant but not always.
There are plenty of unsystematic errors. On p.129, “We” is capitalized in the middle of a sentence. On page 130, a famous trigonometric function is spelled “sign”. On that same page a mysterious sigma appears that is commanded to be strictly negative. Its presence is not explained, but usually sigma in statistics is a standard deviation that cannot be negative. Sure enough, on p.133 it becomes strictly positive. At the middle of p.136 is a string of words that sounds like a Google translation. Overall, the text resembles many of the free rough drafts one can find online more than products of reputable publishers of the past.
So, recommended to those interested in this niche topic, but do use the references to make sure you are working from an error-free statement of any theorems quoted.
After a few years in industry, Robert W. Hayden (firstname.lastname@example.org) taught mathematics at colleges and universities for 32 years and statistics for 20 years. In 2005 he retired from full-time classroom work. He now teaches statistics online at statistics.com and does summer workshops for high school teachers of Advanced Placement Statistics. He contributed the chapter on evaluating introductory statistics textbooks to the MAA's Teaching Statistics.