Customer Reviews

Mathematical Statistics With Applications

5 star:		(13)
4 star:		(7)
3 star:		(9)
2 star:		(6)
1 star:		(7)

 

 

This is an adequate text up until chapter 6. The probability chapter the the discrete probability distributions are great. The concepts and derivations are logically laid out and make sense. Things begin to get frustrating in chapter 4 and really fall apart after chapter 6. After chapter four the author no longer tries to put anything in context. He derives very little and simply states long, cryptic formulas and expects the reader to magicaly understand the big picture and fill in the gaps on their own. He skips over the over 200 years of the development in statictical theory and simply states the results and the student is expected to fill in the gap. The most self evident properties are expounded on in the chapters and the most important and subtle properties are hidden in the exercises or neglected altogether. I am nearly finished with my undergraduate degree in applied mathematics and am mathematicaly mature. I am comfortable with both applied and pure/proof-type mathematics and this text makes my stomach turn. It makes me want to reconsider my major. I am giving this text 2 stars simply because the first 5 chapters are adequate. If you just need a course in probability, this might be the text for you. If you need to move on to statistical inference and you need the big picture/contextual background explained rather than pluging and chuging blindly with nonsensical formulas, then this is not the text for you. Way to drop the ball, Wackerly!

This has been my goto stats book since I bought it for a class in 2002. It's a clear introduction to mathematical statistics. I use it to try to understand some of the more advanced concepts that I'm learning now, but, unfortunately, it is just an introductory book. It does have a lot of information in it, so I still rely on it pretty heavily.

On the flip side, I'm using this book less and less because I bought Wasserman's 'All of Statistics', which is much more compact and has far more concepts in it. 'All of Statistics' is more of a reference tool, instead of a learning tool, though.

If you want to learn statistics, pick up this book and Ross's First Course in Probability. For most non-specialists these books will contain all the probability and statistics you will ever need.

Sorry I can't recommend anything cheaper.

Overall, a good book. Could be a better even after excluding minor details- the ones noticed mentioned below.

Background necessary: Calculus- especially Taylor series, Integration by parts, solving for areas by integration and figuring out their limits; Even with a sufficient background, some proofs are quite rigorous or not well written enough, not sure which sometimes.

Comments based on first 7 Chapters of the book:
Standard deviation- excellently described
Relative frequency- NOT very well described. Makes sense on looking at chart in the book, but readers may forget to look at chart. A good definition for this important term is needed.
p. 43 They mention multinomial expansion before binomial distribution 1 chapter later. Very unnecessary, and doesn't make sense for the general reader to just stick it in there. It's like trying to squeeze information just to try to put something mathematically interesting that is more of a hinderance for learning permutations, combinations, and the multiplication rule. They show it to try to combine the principles together, but to make any sense of the multinomial expansion, besides choosing numbers to do it out, the proof to understand it fully is graduate level mathematics. A big no no for the book!! The least the book could do is expand by showing a specific example of this, and maybe even the proof itself, or just not mention it at all.

Section 2.7, p. 50 intro- too wordy. "relative frequencey of occurrence" in parentheses should probably be taken out for less confusion since a rel. freq. does not have to be based on a conditional probability occurring. Leaving it in leaves the reader at possible ambiguity.
Section 2.9, p. 62 Unnecessarily complicated- 1/5 * 3/4 = answer makes a lot more sense than them breaking it down into an unnecessary 7+ steps = answer.
Binomial Theorem probably could've been presented better. The idea of the binomial expansion and definition 3.7 (binomial distribution theorem) should be explained together right after definition 3.6 (explanation of a binomial experiment) rather than confusing the reader and leaving it off until later on.
p. 102-104 The book does a good job relating some word problems to the real world in good, brief explanations.
p.152 Step function should show hollow points if not the filled end points as well at least- too sloppy.
p. 172 Example 4.9 well done, but makes it sound like = (y- u)/o was intuitively obvious even to the beginner. The book tends to introduce some examples like this to introduce a theory. Just something one needs to get used to. It would be nice if they were able to put a sentence on page 1 about how some conecepts are inrtoduced by example first, but of course not everyone would read it anyway.
p. 188, sec. 4.8- great summary explaining existence for variety of statistical models
Example 5.1, p. 212- not a very good example. The table's correlation to the sample space given is overly ambiguous. Example is confusing, especially since they use the starting point starting from the top right corner instead of the top left corner and show no indication of what stands for what without reader figuring it out. Poorly set up.
p.213 typo- 6/9, not 8/9- tricky to figure out for a beginner
p.225 calculation- just add "= 1" to show solving of one of the integrals. Book sloppily leaves out this simple, but crucial step. A hard read for beginners to notice.
"degrees of freedom (d.f.)" can probably be better and simply defined than the book's "attempts," such as always one less than number of trials or something like that rather than always showing d.f. by notation only.

It's quite arguable if maybe just normal, or normal and t distributions and then central limit theorem should be mentioned in the book first, rather than throwing in all the different kinds of distributions in to learn for Chapter 3 first.

This book is not rigorous at all. If you are looking for rigor, look elsewhere. The proofs are very weak, and the example trite.

Still it is not a total loss. If you don't care about mathematical rigor, this can serve as a decent book.

I wouldn't dream of using it if you are working on a stats based degree.

I'm finishing up an undergraduate course in probability, and I find this book very difficult to follow. I find referencing my combinatorics book (which has almost no probability) significantly more helpful for discrete distributions; the sections on MGFs (which are scattered among three chapters, none of which give a comprehensive explanation of the topic) provide no motivation and are at best unhelpful.
Theorems and definitions are awkwardly stated, and seem as if it was intended to be written for a non-mathematical audience. The problem sets also contribute to this interpretation: most of the problems are computational "given r.v. x with pdf f(x) = ..., find the probailty that X=x given X>y" or other problems to that effect. In other words, the problems give the student no better understanding of the math than memorizing formulas will...
The examples aren't terrible, but aren't enlightening either. Beyond that, the book is horribly formatted (as in, typesetting), and not only are a lot of important concepts hidden in the middle of a dense paragraph, but some of the theorem/definition boxes cross line breaks in awkward ways.

Overall, it's a usable book, but it is too high level for non-math students, and not rigorous enough or precise enough for math students.

After reading through this book and couple of other math stat text like Larsen and Marx, DeGroot, and Berger, etc, this is what I find:

1) The content is shallow. No rigor to mention of. Many proofs are not offered. Proofs offered are always very informal.

2) The authors make easy content overly complex by stating things in many different way, as if this helps learning.

3) The authors absolutely hate "X." They use Y1 and Y2 instead of X and Y, which I think is a much more straightforward and easier notation. So you get the idea, there are subscript to subscript, when in fact the author can use X and Y to avoid additional level of subscript. I read all other textbooks, and this is the only one which uses y1 and y2. That means, if your instructor sucks, you are out of luck, because you cannot reconcile notational difference without investing a lot of library hours. Maybe the author is trying to make students accustom to their notation, so students cannot switch!

4) The author explains easy concepts in details, but skimp through hard concepts. That is sad: because students end up wasting a lot of their time reading what is apparent or easy to understand, but still don't understand the difficult concepts such as mgf and inner workings of gamma functions. I use Berger's Stat Inference textbook as a helper for this textbook!

This book claim it is the most popular; well I say the sales team must be awesome. This is a bad textbook.

This book is a book on mathematical statistics and hence goes further than most entry-level statistics books, which mostly deal with business statistics. This book does not reinvent the wheel, but is goes further where other books end. You will find a mathematical explanation and theorems are proved as well. Soms more advanced topics are moment generating functions and power tests. The consequention is that the learning curve is steeper. At my university, econometrics students use this book, and they couldn't have made a better choice. Logically, since econometricians don't have enough on a book with only a minor focus on formulas.

The examples are insufficient and do not show what formulas the results are derived from or the mathematical or statistical steps that are needed. The proofs also do not tell you the necessary formulas and often tell you to refer to sections that tell you to refer to other sections. Worst of all are the problems, which do not give you any hints and so you won't know if you are doing them with a completely wrong method. The book also does not give some of the necessary formulas to solve many forms of the problems. The distributions and estimators that you will need to work with are usually not given. If your class requires this book, you are going to be pulling your hair out in frustration and you'll need significant amounts of help for about half of the problems.

I've read through Chapter 6 so far on a self-study basis and done lots of the problems. This book was challenging but overall very beneficial to my understanding.

I understood less about probability after reading the first few chapters of this book than before reading it. The wording is extremely vague because the author tries too hard to generalize, using abstract terms such as n, r, x, etc to describe everything and leaving you to decide for yourself which part of the problem these variables apply to in the practice problems (less than half of which have solutions, none of which are comprehensive). Thank goodness for Google and good free math help sites. The biggest problem with this book is the lack of explanations for the practice problems which differ from the examples and are much harder. The hardest practice problems are marked with asterisks but sadly even these are not explained. This is the second Statistics course I've taken and I feel as if this book is confusing everything I learned in the first one. If this book weren't required for class I'd burn it.

Edit: Okay, a year later I've had time to get less angry about this book. In retrospect, it was a good book because it was very comprehensive. It is academically rigorous and anyone wanting to continue in graduate studies in Statistics should use this book. Definitely not for the casual reader. I still think there should have been more/better solutions for the practice problems though, because you learn through practice.