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.

‘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 Source: 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.'

Source: 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 Source: 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 Source: Mathematical Reviews

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

Source: Zentralblatt MATH

'… a useful reference with many elegant proofs.'

David J. Olive Source: Technometrics