An Introduction to Mathematical Statistics and Its Applications (3rd Edition) [Hardcover]

Richard J. Larsen (Author), Morris L. Marx (Author)

Book Description

ISBN-10: 0139223037 | ISBN-13: 978-0139223037 | Publication Date: January 15, 2000 | Edition: 3rd

Using high-quality, real-world case studies and examples, this introduction to mathematical statistics shows how to use statistical methods and when to use them. This book can be used as a brief introduction to design of experiments. This successful, calculus-based book of probability and statistics, was one of the first to make real-world applications an integral part of motivating discussion. The number of problem sets has increased in all sections. Some sections include almost 50% new problems, while the most popular case studies remain. For anyone needing to develop proficiency with Mathematical Statistics.

Editorial Reviews

From the Publisher

Highly structured, this volume allows those with an established mathematics background to pursue a more rigorous, advanced treatment of probability and statistics. --This text refers to an out of print or unavailable edition of this title.

From the Inside Flap

Preface

Changes in this third edition have been primarily motivated by our own teaching experiences as well as by the comments of others who use the text. Technology, though, has also dictated certain revisions. The widespread use of statistical software packages has brought certain topics and concepts to the fore, while diminishing the relevance of others. All in all, we feel that this new edition has a sharper focus and that students will find it more accessible and easier to use.

Many of the major changes come in the middle third of the book, much of which has been rewritten. These are the chapters that make the critical transition from probability to statistics. We have taken a variety of steps to make that material come more alive, ranging from the addition of more helpful examples to the frequent use of computer simulations.

Chapter 4, for example, now addresses more fully the important question of why certain measurements are modeled by particular probability functions. Relationships that exist between pdfs are given more attention, and the connection between theoretical models and sample data is explored in greater depth. Chapter 5 has been restructured. In the new edition, methods of estimation come first and the underlying theory is taken up last. That arrangement makes it easier for instructors to adjust the amount of time spent on estimation to whatever suits their individual needs. In Chapter 6, the principles of decision-making are now introduced in the context of testing Ho: µ = µo rather than Ho: p = po. The result is a more streamlined presentation that avoids the complications inherent in a test statistic whose pdf is discrete.

Positioned between Chapter 7, which deals with the normal distribution, and Chapters 9 through 14, where the various techniques for analyzing data are introduced, is a new chapter on experimental design. Chapter 8 profiles seven of the most frequently encountered "data models." The basic characteristics of each design are discussed as well as the types of questions each seeks to answer. By providing a framework and a theme, Chapter 8 brings cohesion and a sense of order to the chapters that follow.

Chapter 11 (Regression) has also been changed substantially. It now begins with curve-fitting, then introduces the linear model, and eventually concludes with the bivariate normal. Regression "diagnostics" have been added to the new edition, and the various inference procedures associated with the linear model have been explained and delineated more carefully.

Our overriding motivation in deciding which topics to present – and in what order – stem from our objective to write a book that emphasizes the interrelation between probability theory, mathematical statistics, and data analysis. We believe that integrating all three is vitally important, particularly for those students who take only one statistics course during their college careers. Our experience in the classroom has certainly strengthened our faith in this approach: Students can more clearly see the importance of each of the three when viewed in the context of the other two.

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Product Details

• Hardcover: 790 pages
• Publisher: Prentice Hall; 3rd edition (January 15, 2000)
• Language: English
• ISBN-10: 0139223037
• ISBN-13: 978-0139223037
• Product Dimensions: 9.6 x 7.3 x 1.5 inches
• Shipping Weight: 3.1 pounds
• Average Customer Review: 3.4 out of 5 stars  See all reviews (18 customer reviews)
• Amazon Best Sellers Rank: #1,114,864 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

41 of 41 people found the following review helpful:

5.0 out of 5 stars Excellent intro to the mathematics of traditional statistics, March 18, 2005

By 

Bob Carpenter (New York, NY) - See all my reviews

This review is from: An Introduction to Mathematical Statistics and Its Applications (3rd Edition) (Hardcover)

The first half of the book begins with basic discrete and continuous probability theory. It continues with thorough overviews of the basic distributions (normal, Poisson, binomial, multinomial, chi-squared and student-T). The focus is on basic probability and variance analysis, though it briefly covers higher-order moments.

The second half of this book is devoted to hypothesis testing and regression. There is an excellent explanation of the mathematical presuppositions of the various classical experimental methodologies ranging from chi-square to t-tests to generalized likelihood ratio testing. It contains a very nicely organized chapter on general regression analysis, concentrating on the common least squares case under the usual transforms (e.g. exponential, logistic, etc.).

Like many books in mathematics, this introduction starts from first principles in the topic it's introducing, but assumes some "mathematical sophistication". In this case, it assumes you're comfortable with basic definition-example-theorem style and that you understand the basics of multivariate differential equations. I was a math and computer science undergrad who did much better in abstract algebra and set theory than analysis and diff eqs, but I found this book extremely readable. I couldn't have derived the proofs, but I could follow them because they were written as clearly as anything I've ever read in mathematics. I found the explanation of the central limit theorem and the numerous normal approximation theorems for sampling to be exceptionally clear.

The examples were both illuminating and entertaining. One of the beauties of statistics is that the examples are almost always interesting real-world problems, in this case ranging from biological (e.g. significance testing for cancer clusters) to man-made (e.g. Poisson models of football scoring) to physical (e.g. loaded dice). The examples tied directly to the techniques being explored. The exercises were more exercise-like in this book than in some math books where they're a dumping ground for material that wouldn't fit into the body of the text. This book has clearly been tuned over many years of classroom use with real students.

I read this book because I found I couldn't understand the applied statistics I was reading in machine learning and Bayesian data analysis research papers in my field (computational linguistics). In paticular, I wanted the background to be able to tackle books such as Hastie et al.'s "Elements of Statistical Learning" or Gelman et al.'s "Bayesian Data Analysis", both of which pretty much assume a good grounding in the topics covered in this book by Larsen and make excellent follow-on reading.

17 of 20 people found the following review helpful:

2.0 out of 5 stars Confused and confusing, April 11, 2007

By 

Glitzer - See all my reviews

This review is from: Introduction to Mathematical Statistics and Its Applications, An (4th Edition) (Hardcover)

I used this as the text in a sequence on probability and statistics I taught recently, and I soon came to regret this choice. The authors are obviously quite confused about basic concepts. Here are some examples: the "definition" of the median ignores obvious problems with existence and uniqueness; the "proof" of the central limit theorem is thoroughly incomplete; the "theorems" on the tests in Sect. 9.2, 9.3 summarize previous discussions, but the "proofs" of these theorems (we are even referred to an appendix - no small surprise when the statements seem obvious) establish something entirely different; finally, to conclude this (very incomplete) selection, there is the delightful claim that the golden ratio is a transcendental number (which just proves that the authors don't have the slightest idea what a transcendental number really is, but then it might have been wise to avoid the use of the term).

In addition to these blatant problems, the authors' treatment frequently misses the point and/or is confusing.

7 of 7 people found the following review helpful:

5.0 out of 5 stars Excellent introduction to statistics..., September 29, 2002

By 

Jo Totland (Oslo, Oslo Norway) - See all my reviews

This review is from: An Introduction to Mathematical Statistics and Its Applications (3rd Edition) (Hardcover)

This book manages to stay focused on the main ideas all the way through. It uses no more math than what is necessary to derive the proofs of most theorems (although some are omitted). The main ideas of each chapter is introduced before the details are worked out, and summarized at the end of each chapter. The examples and case-studies are usually interesting (sometimes thought-provoking), instead of solely being based on urns and coloured balls. And the exercises range from trivial to interesting...

In short, this is about as good as a textbook gets...