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Elements of Distribution Theory

$54.99 (P)

Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: October 2011
  • availability: Available
  • format: Paperback
  • isbn: 9781107630734

$ 54.99 (P)

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About the Authors
  • This detailed introduction to distribution theory is designed as a text for the probability portion of the first year statistical theory sequence for Master's and PhD students in statistics, biostatistics, and econometrics. The text uses no measure theory, requiring only a background in calculus and linear algebra. Topics range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals and orthogonal polynomials. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book.

    • Provides a comprehensive discussion of the major results of distribution theory at a level not requiring advanced probability theory
    • Contains over 300 examples, 340 exercises and detailed proofs of nearly every result
    • Topics have been chosen in order to prepare the reader for advanced study in statistics, rather than distribution or probability theory
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    Reviews & endorsements

    "The most outstanding aspect of Elements of Distribution Theory is that it solidly fills a gap as an introductory coverage of approximation theory for probability distributions that gracefully avoids measure theory... Severini's proofs are clear, abundant, and illustrate the main techniques."
    SIAM Review

    "A powerful introduction to distribution theory and surveys in its 14 chapters... The book's material is invaluable and has a good presentation."
    Hassan S. Bakouch, Tanta University

    "The exposition is clear and solving the wide variety of exercises at the end of every chapter will be of help in understanding the subject better. Students wishing to learn distribution theory quickly without the use of measure theory will welcome this book."
    Sreenivasan Ravi, Mathematical Reviews

    "... a useful reference with many elegant proofs."
    David J. Olive, Southern Illinois University, Technometrics

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    Product details

    • Date Published: October 2011
    • format: Paperback
    • isbn: 9781107630734
    • length: 528 pages
    • dimensions: 244 x 165 x 28 mm
    • weight: 0.84kg
    • contains: 10 tables 354 exercises
    • availability: Available
  • Table of Contents

    1. Properties of probability distributions
    2. Conditional distributions and expectation
    3. Characteristic functions
    4. Moments and cumulants
    5. Parametric families of distributions
    6. Stochastic processes
    7. Distribution theory for functions of random variables
    8. Normal distribution theory
    9. Approximation of integrals
    10. Orthogonal polynomials
    11. Approximation of probability distributions
    12. Central limit theorems
    13. Approximation to the distributions of more general statistics
    14. Higher-order asymptotic approximations.

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    Elements of Distribution Theory

    Thomas A. Severini

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  • Instructors have used or reviewed this title for the following courses

    • Intro. to Prob. and Stat.
    • Probability Theory ll
    • Topics in Mathematics/Statistics
  • Author

    Thomas A. Severini, Northwestern University, Illinois
    Thomas A. Severini received his PhD in Statistics from the University of Chicago. He is now a Professor of Statistics at Northwestern University. He has also written Likelihood Methods in Statistics. He has published extensively in statistical journals such as Biometrika, the Journal of the American Statistical Association and the Journal of the Royal Statistical Society. He is a member of the Institute of Mathematical Statistics and the American Statistical Association.

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