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Introduction to Mathematical Statistics (7th Edition), by Robert V. Hogg, Joeseph McKean, Allen T Craig
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Introduction to Mathematical Statistics, Seventh Edition, offers a proven approach designed to provide you with an excellent foundation in mathematical statistics. Ample examples and exercises throughout the text illustrate concepts to help you gain a solid understanding of the material.
- Sales Rank: #92120 in Books
- Brand: Brand: Pearson
- Published on: 2012-01-18
- Original language: English
- Number of items: 1
- Dimensions: 9.30" h x 1.20" w x 7.10" l, 2.24 pounds
- Binding: Hardcover
- 640 pages
- Used Book in Good Condition
Most helpful customer reviews
39 of 41 people found the following review helpful.
classic math stat test that I used to prepare for math qualifying exam at the University of Maryland
By Michael R. Chernick
Hogg and Craig is one of my favorite texts. It is an intermediate text in mathematical statistics similar to Mood, Graybill and Boes. I took qualifying exams in mathematics for my Masters Degree at the University of Maryland in the early 1970s. One of the exams I took was in statistics. I had little formal training in statistics at the time. Hogg and Craig was the recommended text for the statistics exam. So I bought it and studied out of it on my own. It was very clear with excellent coverage of methods for deriving distributions for random variables and transformations of random variables. I passed my exams and got my highest grades on the statistics exam even though I had more training in abstract algebra. Hogg and Craig really helped. It has been revised since then to maintain currency with statistical developments but it still has maintained its clarity and usefulness. Most of the other reviews that are critical of it are way off base. I am sure that efforts have been made with the numerous revisions to keep the material up to date. Perhaps some critics are correct that it comes up short on some modern advances in Bayesian statistics and other computer-intensive statistical methods. But that should not tarnish its reputation as a classic text in mathematical statistics.
97 of 112 people found the following review helpful.
Check if you can get an alternative
By Stanislav Kolenikov
There muliple starting points that could generate your interest and need for this book. If you are a math undergrad major, and this is your required reading, stop here, go get it, use it and probably sell second hand -- you won't be doing that much statistics anyway. If you are a grad student with a major other than statistics, and this is a required reading for a class in statisitical inference you are taking at a local Stat department, stop here and go get it anyway; it won't hurt to have it. Everybody else, welcome to continue...
I am now teaching a semester class on introduction to probability theory (the first class in two semester sequence) using this book, and I don't like it very much. It has a little bit strange audience in mind: students who barely have enough math background to do statistics, just the standard 3 semester calculus sequence, but no real analysis and no complex analysis. If you do statistics for living, or consider doing that, you need something more serious measure-theory based (at least that's how I was taught in my grad program, and I see huge advantages in looking down at probability theory from the measure theory prospective).
In other words, it is one of the few books that fill in the gap between all those colorful but very limited and boring "Probability and Statistics for Housewives" the-only-math-class-for-my-general-college-requirement books that steer away from calculus and call a cdf "area under the curve", on one side; and Cramer's Mathematical Methods of Statistics or Kendall/Stuart's Kendall's Advanced Theory of Statistics or Billingsley's Probability and Measure, 3rd Edition (which I also reviewed), on the other side of the rigor spectrum. You get what you paid for: if you invested more into your math training, you would get a much better leverage and understanding of statistics from other books, see below. With this much of calculus, H&C is probably as far as you can go about math statistics.
The material is sequenced in a somewhat awkward manner. Sigma-fields are mentioned in the first chapter, but are not actually used anywhere -- you need measure extension theorems for this stuff to make sense and be useful, and this will shoot you quite far out of the calculus-only class. So, is this an extra stuff that a stat student does not need? Probably not at this level!
Most examples in ealry chapters use well known distributions like uniform, exponential, Poisson, binomial without naming them, and without using the normal distribution that only appears later in the book. I found this confusing, and so will my students, I am afraid. Many of the important concepts, like modes and percentiles of a distribution, or a nice E[u(X)|X]=u(X) shortcut, are hidden in the exercises, so unless you as the instructor stumble across them in the end of a section, or if you are using this book as a reference, then you and/or your students won't see them.
So overall: yes, it is a dated book, it still is an important book for math stat training; but I will only recommend it for somebody in exactly that calculus-only niche. You can use Cramer as a reference; using Hogg and Craig for a reference won't suffice.
Now, what about the alternatives? I am using Wasserman's All of Statistics as a strong supplement in teaching from Hogg and Craig and pulling somewhat nicer examples, exercises, and supplementary results not mentioned in H&C. It also has the same not-so-advanced audience in mind (the course was originally written for computer science students interested in data mining, and a nice extra feature is that Wasserman talks about the computer learning paradigm in parallel to statistical inference paradigm); it is much better written and laid out, with important definitions and theorems clearly highlighted; it structures the material better... BUT! it does not have almost any proofs. However scared you as a student might be of this p-word, your class on mathematical statistics must have enough of those to give you an idea how mathematical statistics works, and how different results in statistics are linked to one another.
Of course another alternative is the classic Cramer "Mathematical Methods of Statistics" textbook that is even more aged (1943) that Hogg and Craig (1958), but it is just better written and more complete. With this one, however, you would need your real analysis, measure theory and complex analysis... or at least some basic understanding of those.
19 of 20 people found the following review helpful.
Intro to Math Stats
By A. Martishius
I am currently a graduate student in Statistics at Miami University of Ohio. For my first and second mathematical statistics courses, we are using this text.
This is a really great book. It is fairly short, and each section is on average only 2-3 pages, but those 2-3 pages are absolutely packed with good stuff. Usually there will be a short introductory paragraph on the topic, and then the authors get right into theorems and examples. There are usually 2-3 theorems and 2-3 examples per section, and they are all organized very well.
The theorems always appear in an appropriate place in the section (i.e. it makes sense in the flow of the explanation of the topic). They are always set up in a manner which makes them easy to understand, and proof of each theorem follows its declaration. If the theorem is too difficult to understand or too long to reasonably fit a paragraph, the authors cite the original publication in which the theorem appeared. Additionally, there are no extraneous proofs, and each one of them is essential to understanding the course material.
The examples usually follow the theorems and will use the result of the theorem as a direct tool to solve the example. Most of the time, the examples will be pretty similar to the homework problems, and provide good hints that will lead you in the right direction when you are attempting the homework. The authors are never trying to be "impressive" with their examples; the clear objective is to help you understand the material without being unnecessarily complicated and/or skipping steps.
The homework is also excellent. It is challenging enough to force you to be competent with all of the material presented, but never leaves you at one of those infamous "google search" dead-ends. Usually the first 8-10 problems in each section are relatively easy if you are grasping the material, and there are lots of answers in the back of the book to aid you. As you get to the end of the homework problems in the section, you will be looking at things that are highly theoretical, are proofs, or require critical thinking. The authors' response to this extra challenge is really the greatest thing I have ever found in a college-level textbook. If a homework problem requires using a "trick" that is beyond the common-sense level, the authors provide a helpful "hint" to point you in the right direction. It is certainly possible to solve the problem without using the hint, but after doing a semester of problems, I can tell you that the hints will save you hours of frustration that you would have spent trying to figure out what little "trick" you were supposed to use to solve the problem.
All in all, I think this is the best mathematics textbook I've ever had, a close second behind "Introductory Abstract Algebra" by Joe Gallian. I think if you are interested in statistics at the graduate level, this is THE BOOK to get you started. I honestly cannot think of any criticisms that I have of this book, and I truly believe it's possible to learn the foundation of mathematical statistics with this book, even if you don't have a professor available to you.
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