Mitra, Sujit Kumar
(1969)
*Some characteristic and noncharacteristic properties of the Wishart distribution*
Sankhya - Series A, 31
(1).
pp. 19-22.
ISSN 0581-572X

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Official URL: http://sankhya.isical.ac.in/search/31a1/31a1003.ht...

## Abstract

If the elements of a matrix $S$ follow a central Wishart distribution $W_{k}(n,\Sigma)$ and $a'\Sigma a\neq 0$ it is wellknown that $a'Sa/a'\Sigma a$ is distributed as a chi-square on $\nu$ d.f.. Further $a'\Sigma a=1 \Longrightarrow a'Sa=0$ with probability one. The object of this paper is to show through a counter-example that the converse of this result is not necessarily true unless $\Sigma$ is of rank one. It is shown, however, that if for every matrix $L$, such that $L\Sigma L'=I$, the diagonal elements of $LSL'$ are distributed as independent chisquare variables on $\nu$ d.f., then $S$ has a central Wishart distribution $W_{k}(\nu,\Sigma)$.

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

ID Code: | 32035 |

Deposited On: | 30 Mar 2011 12:55 |

Last Modified: | 30 Mar 2011 12:55 |

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