© 2017

Probability for Statisticians


Part of the Springer Texts in Statistics book series (STS)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Galen R. Shorack
    Pages 1-21
  3. Galen R. Shorack
    Pages 23-38
  4. Galen R. Shorack
    Pages 39-66
  5. Galen R. Shorack
    Pages 67-87
  6. Galen R. Shorack
    Pages 89-105
  7. Galen R. Shorack
    Pages 107-126
  8. Galen R. Shorack
    Pages 127-148
  9. Galen R. Shorack
    Pages 149-191
  10. Galen R. Shorack
    Pages 193-223
  11. Galen R. Shorack
    Pages 225-270
  12. Galen R. Shorack
    Pages 297-343
  13. Galen R. Shorack
    Pages 345-385
  14. Galen R. Shorack
    Pages 387-399
  15. Galen R. Shorack
    Pages 401-415
  16. Back Matter
    Pages 417-510

About this book


This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians—a textbook for courses in probability for students in mathematical statistics. It is recommended to anyone interested in the probability underlying modern statistics, providing a solid grounding in the probabilistic tools and techniques necessary to do theoretical research in statistics. For the teaching of probability theory to post graduate statistics students, this is one of the most attractive books available.

Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. Martingale coverage includes coverage of censored data martingales. The text includes measure theoretic preliminaries, from which the authors own course typically includes selected coverage. 

This is a heavily reworked and considerably shortened version of the first edition of this textbook. "Extra" and background material has been either removed or moved to the appendices and important rearrangement of chapters has taken place to facilitate this book's intended use as a textbook.

New to this edition:

  • Still up front and central in the book, Chapters 1-5 provide the "measure theory" necessary for the rest of the textbook and Chapters 6-7 adapt that measure-theoretic background to the special needs of probability theory
  • Develops both mathematical tools and specialized probabilistic tools
  • Chapters organized by number of lectures to cover requisite topics, optional lectures, and self-study
  • Exercises interspersed within the text
  • Guidance provided to instructors to help in choosing topics of emphasis


Brownian Motion law of large numbers martingale probability theory distribution central limit theorem measure theory

Authors and affiliations

  1. 1.Department of StatisticsUniversity of WashingtonSeattleUSA

About the authors

Galen Shorack, PhD, is Professor Emeritus in the Department of Statistics (of which he was a founding member) and Adjunct Professor in the Department of Mathematics at the University of Washington, Seattle.  He received his Bachelor of Science and Master of Science degrees in Mathematics from the University of Oregon and his PhD in Statistics from Stanford University.  Dr. Shorack's research interests include limit theorems in statistics, the theory of empirical processes, trimming-Winsorizing, and regular variation.  He has served as Associate Editor of the Annals of Mathematical Statistics (Annals of Statistics) and is Fellow of the Institute of Mathematical Statistics.

Bibliographic information

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“It discusses measure theoretic probability from the viewpoint of what a theoretical statistician needs to know, and includes many details that an applied statistician may need to look up on occasion. Reading it frequently feels like you are sitting next to the author, with him pointing out the important parts, and suggesting how to think about things. I enjoyed that aspect very much, and it helps to solidify the readers understanding.” (Peter Rabinovitch, MAA Reviews, January, 2018)