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Elements of Distribution Theory


Part of Cambridge Series in Statistical and Probabilistic Mathematics

  • Date Published: May 2012
  • availability: Available
  • format: Paperback
  • isbn: 9781107630734

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About the Authors
  • This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered 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, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.

    • 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 text contains a wealth of interesting and useful material, most of which does not work its way into standard first courses in probability or mathematical statistics.' Fred Huffer, Journal of the American Statistical Association

    '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 … The book's material is invaluable and has a good presentation … meets its goal and [serves] all who are interested in statistics, and so it is strongly recommended to libraries.' Hassan S. Bakouch, Journal of the Royal Statistical Society

    '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

    'This is a very good book on statistical distribution theory.' Zentralblatt MATH

    '… a useful reference with many elegant proofs.' David J. Olive, Technometrics

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    Product details

    • Date Published: May 2012
    • 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.

  • Resources for

    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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