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On a New Class of Bounds for the Distribution of Quadratic Forms in Normal Variates

Leon Jay Gleser
Journal of the American Statistical Association
Vol. 67, No. 339 (Sep., 1972), pp. 655-659
DOI: 10.2307/2284460
Stable URL: http://www.jstor.org/stable/2284460
Page Count: 5
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On a New Class of Bounds for the Distribution of Quadratic Forms in Normal Variates
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Abstract

Except in special cases, the distribution of a quadratic form Q in the normal random vector y cannot be expressed in closed form. However, bounds on the cumulative distribution of Q have been obtained by many authors. This article derives a new class of such bounds by means of a certain mixture representation for the distribution of Q. It is shown how the results apply to the problem of finding the distribution of ratios of independent quadratic forms in normal variates.

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