Elements of Distribution Theory

This introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics and researchers using statistical methods.

Thomas A. Severini (Author)

9780521844727, Cambridge University Press

Hardback, published 8 August 2005

528 pages, 10 tables 354 exercises
25.4 x 17.8 x 2.9 cm, 1.075 kg

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

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.

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.

Subject Areas: Probability & statistics [PBT], Mathematics [PB], Economic statistics [KCHS], Econometrics [KCH]