Mitra, Sujit Kumar
(1970)
*A density-free approach to the matrix variate beta distribution*
Sankhya - Series A, 32
(1).
pp. 81-88.
ISSN 0581-572X

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Official URL: http://sankhya.isical.ac.in/search/32a1/32a1007.ht...

## Abstract

Let $ S_1\sim W_k(n_1;\boldsymbol\Sigma)$ and $ S_2\sim W_k(n_2,\boldsymbol\Sigma)$ be independent Wishart matrices and $\boldsymbol\Sigma$ be p.d. Consider $ S= S_1+ S_2$ and define $ U=(S)ˆ{-½} S_1[( S)ˆ{-½}]$, where $( S)ˆ{½}$ is the unique lower triangular matrix with positive diagonal elements, such that $( S)ˆ{½}[( S)ˆ{½ }]'= S$, and $( S)ˆ{-½}$ is the inverse of $( S)ˆ{½}$. The joint distribution of the element of the symmetric matrix $ U$ is said to be `matrix variate beta' and is denoted by the symbol $B_k(n_½,n_2/2)$. Several interesting properties of this distribution are obtained in this paper.

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Source: | Copyright of this article belongs to Indian Statistical Institute. |

ID Code: | 32038 |

Deposited On: | 30 Mar 2011 12:55 |

Last Modified: | 30 Mar 2011 12:55 |

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