Book contents
- Frontmatter
- Contents
- List of Illustrations
- Preface
- 1 Introduction
- 2 The Characteristic Function
- 3 Linear Combinations, Products, and Ratios
- 4 Bivariate Generalizations and Related Distributions
- 5 Multivariate Generalizations and Related Distributions
- 6 Probability Integrals
- 7 Probability Inequalities
- 8 Percentage Points
- 9 Sampling Distributions
- 10 Estimation
- 11 Regression Models
- 12 Applications
- References
- Index
Preface
Published online by Cambridge University Press: 04 May 2010
- Frontmatter
- Contents
- List of Illustrations
- Preface
- 1 Introduction
- 2 The Characteristic Function
- 3 Linear Combinations, Products, and Ratios
- 4 Bivariate Generalizations and Related Distributions
- 5 Multivariate Generalizations and Related Distributions
- 6 Probability Integrals
- 7 Probability Inequalities
- 8 Percentage Points
- 9 Sampling Distributions
- 10 Estimation
- 11 Regression Models
- 12 Applications
- References
- Index
Summary
Multivariate t distributions have attracted somewhat limited attention of researchers for the last 70 years in spite of their increasing importance in classical as well as in Bayesian statistical modeling. These distributions have been perhaps unjustly overshadowed – during all these years – by the multivariate normal distribution. Both the multivariate t and the multivariate normal are members of the general family of elliptically symmetric distributions. However, we feel that it is desirable to focus on these distributions separately for several reasons:
Multivariate t distributions are generalizations of the classical univariate Student t distribution, which is of central importance in statistical inference. The possible structures are numerous, and each one possesses special characteristics as far as potential and current applications are concerned.
Application of multivariate t distributions is a very promising approach in multivariate analysis. Classical multivariate analysis is soundly and rigidly tilted toward the multivariate normal distribution while multivariate t distributions offer a more viable alternative with respect to real-world data, particularly because its tails are more realistic. We have seen recently some unexpected applications in novel areas such as cluster analysis, discriminant analysis, multiple regression, robust projection indices, and missing data imputation.
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- Multivariate T-Distributions and Their Applications , pp. xi - xiiPublisher: Cambridge University PressPrint publication year: 2004