Elements of Distribution Theory

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August 2005



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.


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.


Thomas A. Severini received his Ph.D. 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.


'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
EAN: 9780521844727
ISBN: 052184472X
Untertitel: 'Cambridge Series in Statistica'. Sprache: Englisch.
Erscheinungsdatum: August 2005
Seitenanzahl: 515 Seiten
Format: gebunden
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