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THE LIMITING FORM OF THE NON‐CENTRAL WISHART DISTRIBUTION 1,2
Author(s) -
Jensen D.B.
Publication year - 1972
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1972.tb00331.x
Subject(s) - wishart distribution , limiting , distribution (mathematics) , mathematics , multivariate statistics , inverse wishart distribution , asymptotic distribution , gaussian , matrix t distribution , rayleigh distribution , combinatorics , statistics , physics , mathematical analysis , probability density function , quantum mechanics , mechanical engineering , estimator , engineering
SUMMARY Let S ( p × p ) have a Wishart distribution ‐with v degrees of freedom and non‐centrality matrix θ= [θ jK ] ( p × p ). Define θ 0 = min {| θ jk |}, let θ 0 →∞, and suppose that | θ jK | = 0(θ o ). 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.