Elements Of Distribution Theory

Description:
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.

Review:
'This is a very good book on statistical distribution theory.' Zentralblatt MATH ' ... a powerful introduction to distribution theory ... The book's material is invaluable ... meets its goal and severs all who are interested in statistics, and so it is strongly recommended to libraries.' Journal of the RSS

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.

Author Biography:
Thomas A. Severini received his Ph.D. in Statistics from the University of Chicago. He is now a Professor of Statistics at Northwestern University. Aside from this book, he has also written Likelihood Methods in Statistics, published by Oxford University Press. He's published extensively in statistical journals such as Biometrika, Journal of the American Statistical Association, and Journal of the Royal Statistical Society. He is a member of the Institute of Mathematical Statistics and the American Statistical Association.