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Elements of Distribution Theory

Librairie Eyrolles - Paris 5e
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Elements of Distribution Theory

Elements of Distribution Theory

- Collection Cambridge series in statistical and probabilistic mathematics

514 pages, parution le 08/12/2005

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
Voir tout
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Caractéristiques techniques du livre "Elements of Distribution Theory"

  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

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