ON THE WISHART DISTRIBUTION IN STATISTICS
成果类型：
Article
署名作者：
AITKEN, AC
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/36.1-2.59
发表日期：
1949
页码：
5962
关键词：
摘要：
A lemma due to Siegel is stated and an elegant proof given. It is shown that the lemma may be used to go from the Laplace transform or moment-generating function of the estimates of 2d order moments of a k-variate normal population to the vVishart distr. function. A derivation of the moment-generating function of the estimates is given for the ordinary case and also for the case in which a polynomial rather than a constant is fitted to the variates. In the latter case, it is shown that the Wishart distr. still holds with (n-1) replaced by (n-k), provided all variates are fitted to the same orthonormal basis of k independent functions.
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