Elements of Distribution Theory

Thomas A. Severini - Collection Cambridge series in statistical and probabilistic mathematics

514 pages, parution le 08/12/2005

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Résumé

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.

Provides a comprehensive discussion of the major results of distribution theory at a level not requiring advanced probability theory

There are over 300 examples and 340 exercises, and it contains detailed proofs of nearly every result

The topics are chosen in order to prepare the reader for advanced study in statistics, rather than distribution or probability theory easy to understand

Sommaire

Preface
Properties of probability distributions
Conditional distributions and expectation
Characteristic functions
Moments and cumulants
Parametric families of distributions
Stochastic processes
Distribution theory for functions of random variables
Normal distribution theory
Approximation of integrals
Orthogonal polynomials
Approximation of probability distributions
Central limit theorems
Approximation to the distributions of more general statistics
Higher-order asymptotic approximations
Appendix 1: Integration with Respect to a Distribution Function
Appendix 2: Basic Properties of Complex Numbers
Appendix 3: Some Useful Mathematical Facts
References
Name Index
Subject Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Thomas A. Severini
Collection	Cambridge series in statistical and probabilistic mathematics
Parution	08/12/2005
Nb. de pages	514
Format	18 x 26
Couverture	Relié
Poids	1064g
Intérieur	Noir et Blanc
EAN13	9780521844727
ISBN13	978-0-521-84472-7