Elements of Distribution Theory
Elements of Distribution Theory
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
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
Product details
October 2011Paperback
9781107630734
528 pages
244 × 165 × 28 mm
0.84kg
10 tables 354 exercises
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.
