An Introduction to Mathematical Statistics and Its Applications

by Richard J. Larsen, Morris L. Marx

Noted for its integration of real-world data and case studies, this guide offers sound coverage of the theoretical aspects of mathematical statistics. It demonstrates how and when to use statistical methods, while reinforcing the calculus that readers have already mastered. Presents standard statistical techniques in a mathematical context, allowing the reader to see the underlying hypotheses for the applications. Uses case studies and practical worked-out examples to motivate statistical reasoning and demonstrate the application of statistical methods to a wide variety of real-world situations. Discusses practical problems in the application of the ideas covered in each chapter, as well as common misunderstandings or faulty approaches. Revised Minitab sections now conform to the Version 14, the latest release. For anyone interested in learning more about mathematical statistics.

Genres: Mathematics, Textbooks, Economics

920 pages, Hardcover

First published January 1, 1981

Reviews

[William Schram · Rating 4 out of 5]

A well-done book on statistics that includes all the theorems I can think of. Goes into situations and proofs that require Calculus, but that isn't really a big deal.

The book is pretty standard, though I don't know how good MINITAB is since I have neither used nor heard of it. Apparently, it is a statistics package. Then again, I suppose I could modify it for SciPy or something along those lines.

In any case, this book is really good at explaining things. My only problem is that my grounding in Calculus is so tenuous that I don't really have a grasp of the proofs presented. All I can do is smile and nod at the results. So I probably need to go back to Calculus and try to learn that on my own.

[L. C. Nielsen · Rating 1 out of 5]

Terrible. Doesn't explain the mathematics indepth, and is poor at giving an intuitive understanding of statistics. One of the worst textbooks I have had the displeasure of reading.

[Dan]

A very gentle introduction to statistics.

[James Povilonis · Rating 5 out of 5]

This book is an excellent bridge between introductory (more intuitive) statistics and a more theoretical, mathematical statistics. It spans so many topics, providing a great rhetorical and mathematical introduction to every single one. Every topic is approached starting with the motivation - what is the problem we are trying to solve? And the math is steadily developed with ample explanation, so that everything feels natural and well-placed. This gives the reader a secure footing in each topic, so that they can later on pick up a more "serious" mathematical statistics book and understand the thinking and motivation behind each topic. I highly recommend this textbook.

[Q* := Q - {0} · Rating 5 out of 5]

This probably should be a four-star(-plus) rating because the stats section was a bit underwhelming and felt a bit rushed—the LaTeX formatting, too, was a bit unwieldily and inelegant in various spots—but I "rounded up" due to the wonderful chapters on probability, the quality of the examples/test cases, the clear exposition, and the proofs. I've read Rosanov and a bunch of other texts on probability theory, but Larsen and Marx's tome does more than enough to make room for itself. I can't remember the last time I read a textbook where the marriage between theory and practice was so effective, immediate, entertaining, and illuminating. This is an achievement.

Yes, you need the (basic elements of the) machinery of calculus to understand what's happening in the first 2/3 of the book, but its inaccessibility to beginners and casual readers is counterbalanced by what it offers those prepared to engage the material. If you're interested in the mathematics of probability (or you're taking stats with a heavy probability component), this would be a fine companion text to supplement your learning.

[Derek · Rating 2 out of 5]

Terribly organized and written. Read Statistics by Freedman, Pisani, and Purves instead.

[George Maris · Rating 5 out of 5]

The best introductory statistics book ever.