Customer Reviews

Introduction to Mathematical Statistics

5 star:		(22)
4 star:		(6)
3 star:		(9)
2 star:		(8)
1 star:		(13)

 

 

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.

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.

Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)

I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."

Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))

Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)

The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))

Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])

I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as the older editions. I recommend it to others with no reservations.

I worked with an earlier version of this text. The text is
geared for math majors. There are many practical examples;
however, the more theoretical examples are elusive at best.
Coverage of the basic laws of probability is good. The examples
dealing with continuous random variables require some prior
knowledge of intermediate calculus which should be no problem
for math majors or engineers. The book benefited me when I
took and passed the Fundamentals of Engineering Examination.
In addition, I've taught statistics several times.
This work is geared for the above-average student. In some
areas, it could be supplemented with the Schaum's Statistics
Outline.

I am a bit puzzled by the numerous low reviews of this book. I suspect that these reviews may be more due to the fact that this book is being mis-used in courses than due to anything lacking in the book itself. This book requires a certain mathematical sophistication and background, and would be absolutely inappropriate for students without this background. My only criticism of this book is that it is strictly classical. It does not explore the Bayesian way of looking at things, does not make any connections to information theory. Although it covers a few nonparametric techniques, it does not integrate them into the discussion from the beginning. Also, there is not as much discussion of theory.

This book is a classic book on statistics. It has been updated with a new author, but the book is essentially the same as the original by Hogg and Craig. It is a good book, but it is hardly modern. Nowadays, this book is being replaced by books like the Casella and Berger. Honestly? I find the Casella and Berger to be inferior to this book. This book may come across as a bit more dry at first, but as one gets into the later chapters, it remains its clarity, whereas the Casella and Berger loses it. In addition, I think the Casella & Berger is more caught up in tedious manipulations than this book is. The coverage of topics is similar. I also find the exercises in this book to be better.

What does this book require? This is not an introductory book, even to a mathematician. I would recommend a prior course in probability, and a number of other rigorous math courses; a course in mathematical analysis/advanced calculus would be helpful. If students are being advised to take courses using this textbook, and they do not have this background, then I would argue that the professors or advisors are to blame--not this textbook. Students nowadays are too passive and listen too readily to the advice of others or the policies and course requirements in a department--they would do well to believe more in their own abilities and question advice and policies, instead of pointing the blame at a textbook when they do not succeed.

I think this book's use in a course is defensible, although I do not think it is an ideal book for this purpose. I think this book is more useful for self-study (for someone who already knows some of the material) than it is as a textbook. I prefer the book by Rice on Mathematical Statistics, because I think it covers a similar amount of material but is more accessible, and also more practically-oriented, but without sacrificing coverage of the theory. I find the book by Casella and Berger to be notably inferior. Other books worth looking at which are quite different include the book by Welsh "Aspects of Statistical Inference", which does not cover the theory but would show one how to use it, or the book "All of Statistics" by Larry Wasserman, which is shorter but overviews more material than is covered in this book.

Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)

I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."

Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))

Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)

The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))

Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])

I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as the older editions. I recommend it to others with no reservations.

Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)

I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."

Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))

Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)

The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))

Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])

I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as the older editions. I recommend it to others with no reservations.

Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)

I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."

Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))

Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)

The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))

Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])

I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as were the older editions. I recommend it to others with no reservations.

Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)

I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."

Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))

Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)

The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))

Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])

I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as were the older editions. I recommend it to others with no reservations.

Excellent Introduction to Mathematical Statistics

Introduction to Mathematical Statistics

by Robert Hogg and Allen Craig (First Edition through Fifth Edition)
by Robert Hogg, Joseph McKean and Allen Craig (Sixth Edition)

Publication History:

First Edition
* (Year 1959)
* (245 pages)

Second Edition
* (Year 1965)
* (383 pages)

Third Edition
* (Year 1970)
* (415 pages)

Fourth Edition
* (Year 1978)
* (448 pages)
* (ISBN-10: 0029789907)
* (ISBN-13: 978-0029789902)
* (ISBN-10: 0023557109)
* (ISBN-13: 978-0023557101)

Fifth Edition
* (Year 1994)
* (576 pages)
* (ISBN-10: 0023557222)
* (ISBN-13: 978-0023557224)

Sixth Edition
* (Year 2004)
* (692 pages)
* (ISBN-10: 0130085073)
* (ISBN-13: 978-0130085078)

I read the third edition when it was first published. I was in school; I used it in an undergraduate class. Since then "Hogg and Craig" and now "Hogg; McKean and Craig" has been a regular reference work for me.

The only editions I've only read completely are the third edition and the sixth edition; I have used the fifth edition as a reference source since it was published first published. The coverage of mathematical statistics is concise and very thorough in all the editions.

The chapter on "Sufficient Statistics" is the clearest presentation I have ever seen. The chapter "Theory of Statistical Tests" is a very advanced treatment but very easy to use for any practitioner.

Another of my favorites is the last chapter on "Non-Parametric Statistics."

The following are good backup references and books that expand on ideas covered in "Introduction to Mathematical Statistics."

Other references on mathematical Statistics:
* (Mathematical Methods of Statistics. (PMS-9))
* (Introduction to Probability Theory and Statistical Inference (Wiley Series in Probability and Mathematical Statistics. Probability and Mathematical Statistics))
* (Random Variables and Probability Distributions (Cambridge Tracts in Mathematics))

Probability Theory
* (An Introduction to Probability Theory and its Applications: Volume I (Third Edition))
* (An Introduction to Probability Theory and Its Applications, Volume 2)

The Linear Model
* (Linear Models for Multivariate, Time Series, and Spatial Data (Springer Texts in Statistics))
* (Regression Analysis: Theory, Methods, and Applications (Springer Texts in Statistics))

Non-Parametric Models
* (All of Nonparametric Statistics (Springer Texts in Statistics))
* (Nonparametric Statistical Methods, 2nd Edition)
* ([[ASIN:B000VI5U4W Analyzing Categorical Data (Springer Texts in Statistics)(Wiley Series in Probability and Statistics)]])

I've enjoyed this book since I first read it in 1971. The new edition is every bit as practical and enjoyable as the older editions. I recommend it to others with no reservations.