Thomas A. Severini

Elements of Distribution Theory

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Seitenzahl: 528
• Erscheinungstermin: 2. Oktober 2015
• Englisch
• Abmessung: 260mm x 183mm x 33mm
• Gewicht: 1177g
• ISBN-13: 9780521844727
• ISBN-10: 052184472X
• Artikelnr.: 21709668

Autorenporträt

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.

Inhaltsangabe

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.

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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.