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July, 1975 Tail Probabilities of Noncentral Quadratic Forms
Rudolf Beran
Ann. Statist. 3(4): 969-974 (July, 1975). DOI: 10.1214/aos/1176343199


Let $S(b) = \Sigma r\sigma r^2Xr^2(nr,br^2)$ be a positive linear combination of independent noncentral chi-square random variables. This note derives two representations for the tail probabilities P[S(b) >x], a Taylor series in the noncentrality parameters and a limiting form of this series for large x. An application of the latter result to statistical tests of Cramer-von Mises type is discussed.


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Rudolf Beran. "Tail Probabilities of Noncentral Quadratic Forms." Ann. Statist. 3 (4) 969 - 974, July, 1975.


Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0346.60012
MathSciNet: MR381122
Digital Object Identifier: 10.1214/aos/1176343199

Primary: 60E05
Secondary: 62G10

Keywords: Cramer-von Mises tests , noncentral quadratic forms , tail probabilities

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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