## Matrix Variate DistributionsUseful in physics, economics, psychology, and other fields, random matrices play an important role in the study of multivariate statistical methods. Until now, however, most of the material on random matrices could only be found scattered in various statistical journals. Matrix Variate Distributions gathers and systematically presents most of the recent developments in continuous matrix variate distribution theory and includes new results. After a review of the essential background material, the authors investigate the range of matrix variate distributions, including: With its inclusion of new results, Matrix Variate Distributions promises to stimulate further research and help advance the field of multivariate statistical analysis. |

### What people are saying - Write a review

User Review - Flag as inappropriate

This work is the most complete reference in existence for matrix-variate distributions.

### Contents

PRELIMINARIES | 1 |

MATRIX VARIATE NORMAL DISTRIBUTION | 55 |

WISHART DISTRIBUTION | 87 |

MATRIX VARIATE tDISTRIBUTION | 133 |

MATRIX VARIATE BETA DISTRIBUTIONS | 165 |

MATRIX VARIATE DIRICHLET DISTRIBUTIONS | 199 |

DISTRIBUTION OF QUADRATIC FORMS | 225 |

MISCELLANEOUS DISTRIBUTIONS | 279 |

GENERAL FAMILIES OF MATRIX VARIATE | 311 |

GLOSSARY OF NOTATIONS AND ABBREVIATIONS | 331 |

343 | |

364 | |

### Common terms and phrases

characteristic function characteristic roots confluent hypergeometric function constant matrix COROLLARY defined denoted density function derived det(E Dirichlet distribution distribution with parameters gamma Gupta Hence i-distribution independently distributed integral invariant measure Jacobian joint density joint p.d.f. Khatri Laplace transform Lemma lower triangular matrix matrix of rank matrix variate beta matrix variate Dirichlet matrix variate distribution matrix variate normal matrix with positive matrix X p x n Ms(Z n x n noncentral matrix variate nonsingular obtained orthogonal matrix p x m p x p p.d.f. is given partition positive diagonal elements probability element Prove Theorem quadratic forms random matrix Re(a result follows right spherical Rpxm Stiefel manifold stochastically independent Substituting symmetric matrix symmetric positive definite THEOREM type II distribution variate beta type variate normal distribution vec(X Wishart distribution Wishart matrix Wp(n zonal polynomials

### Popular passages

Page 353 - Reprinted in Statistical Inference in Elliptically Contoured and Related Distributions (KT Fang and TW Anderson, eds.), Allerton Press, New York.