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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.
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.
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 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.
'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
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