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Preliminaries

  • A. K. Gupta
  • T. Varga
Chapter
  • 186 Downloads
Part of the Mathematics and Its Applications book series (MAIA, volume 240)

Abstract

Matrix variate distributions have been studied by statisticians for a long time. The first results on this topic were published by Hsu and Wishart. These distributions proved to be useful in statistical inference. For example, the Wishart distribution is essential when studying the sample covariance matrix in the multivariate normal theory. Random matrices can also be used to describe repeated measurements on multivariate variables. In this case, the assumption of the independence of the observations, a commonly used condition in statistical analysis, is often not feasible. When analyzing data sets like these, the matrix variate elliptically contoured distributions can be used to describe the dependence structure of the data. This is a rich class of distributions containing the matrix variate normal, contaminated normal, Cauchy and Student’ s t-distributions. The fact that the distributions in this class possess certain properties, similar to those of the normal distribution, makes them especially useful. For example, many testing procedures developed for the normal theory to test various hypotheses can be used for this class of distributions, too.

Keywords

Probability Density Function Random Matrix Orthogonal Matrix Matrix Variate Generalize Inverse 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • A. K. Gupta
    • 1
  • T. Varga
    • 2
  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA
  2. 2.AB-AEGON General Insurance CompanyBudapestHungary

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