ASTIA-AD18066
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ASTIA-AD18066 On the Distribution of Quadratic Forms
One could easily å•aJt1fy the Btudy of the diatribution Of quadretlc forma from the standpolnt that many of the teøta in gtetietlcg are based oa the Of quantities which can be thought Of special cane Of either a quadratic form or func— tlons of quaratlc forms. The applicationa ere too ntne-—ous to however, ve a fev as Illustrationø. (1) The distribution of a definite quadratic fom vbere the componenta have a multi— varlete normal åiøt.ribution. (11) The proble Of finding the puer func— tion of the chi—aquare øtati3tic, for large sampleB, can be reduced to of finding the dløtributlon Of a positive definlte quedratlc form In non—central normal (111)The distribution Of a form Of the aerial corre2at10n eoefflcient can be expregeed In terms Of the dløtrlbution of a ratio of two qu*dratic fomø. See Andereon r 1_71 (iv) Of special Import:nce is von Neruanr:t8 r 2.9_7, C 20_7, the ratio Of
(v) the meza successive difference to the vartn.nce, to teet whether obEer'Et10ra are Independent or whether A trend exists. D'Ebi.•: Vateon szetietic tect the error terra for Independence In lea" regreseion. (VI) r 12_7, says, "Asgum!ng a nornl Cor the the mathcætlcal for an eet±mAtion theory Of etccbastlc ßoceasee is the etudy of the dist2•ibutiong Of cetain quadratic foms In normal variables". The problem Kocpr•ns considers la that og estimating the Serial correlation In a etationary Btochaøtic proceee . (Vli) Tc hy?0theeee concerning variance components In the analysis Of variance, ve requlre the Of an indefinite qwdratlc form.
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