Elements of Distribution Theory

Thomas A. Severini received his PhD 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.

• 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.

'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