THE LIMITING FORM OF THE NON‐CENTRAL WISHART DISTRIBUTION1,2
- 1 April 1972
- journal article
- Published by Wiley in Australian Journal of Statistics
- Vol. 14 (1) , 10-16
- https://doi.org/10.1111/j.1467-842x.1972.tb00331.x
Abstract
SUMMARY: Let S (p×p) have a Wishart distribution ‐with v degrees of freedom and non‐centrality matrix θ= [θjK] (p×p). Define θ0= min {| θjk |}, let θ0→∞, and suppose that | θjK | = 0(θo). Then the limiting form of the standardized non‐central distribution, as θ while n̈ remains fixed, is a multivariate Gaussian distribution. This result in turn is used to obtain known asymptotic properties of multivariate chi‐square and Rayleigh distributions under somewhat weaker conditions.Keywords
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