Symmetric multivariate and related distributions

著者

書誌事項

Symmetric multivariate and related distributions

Kai-Tai Fang, Samuel Kotz, Kai Wang Ng

（Monographs on statistics and applied probability, 36）

Chapman and Hall, 1990

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注記

Bibliography: p. [202]-212

Includes index

内容説明・目次

内容説明

Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory.

目次

  • Part 1 Preliminaries: construction of symmetric multivariate distributions
  • notation of algebraic entities and characteristics of random quantities
  • the "d" operator
  • groups and invariance
  • dirichlet distribution
  • problems 1. Part 2 Spherically and elliptically symmetric distributions: introduction and definition
  • marginal distributions, moments and density
  • marginal distributions
  • moments
  • density
  • the relationship between (phi) and f
  • conditional distributions
  • properties of elliptically symmetric distributions
  • mixtures of normal distributions
  • robust statistics and regression model
  • robust statistics
  • regression model
  • log-elliptical and additive logistic elliptical distributions
  • multivariate log-elliptical distribution
  • additive logistic elliptical distributions
  • complex elliptically symmetric distributions. Part 3 Some subclasses of elliptical distributions: multiuniform distribution
  • the characteristic function
  • moments
  • marginal distribution
  • conditional distributions
  • uniform distribution in the unit sphere
  • discussion
  • symmetric Kotz type distributions
  • definition
  • distribution of R(2)
  • moments
  • multivariate normal distributions
  • the c.f. of Kotz type distributions
  • symmetric multivariate Pearson type VII distributions
  • definition
  • marginal densities
  • conditional distributions
  • moments
  • conditional distributions
  • moments
  • some examples
  • extended Tn family
  • relationships between Ln and Tn families of distributions
  • order statistics
  • mixtures of exponential distributions
  • independence, robustness and characterizations
  • problems V. Part 6 Multivariate Liouville distributions: definitions and properties
  • examples
  • marginal distributions
  • conditional distribution
  • characterizations
  • scale-invariant statistics
  • survival functions
  • inequalities and applications.

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