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.
@article{1176343199,
author = {Beran, Rudolf},
title = {Tail Probabilities of Noncentral Quadratic Forms},
journal = {Ann. Statist.},
volume = {3},
number = {1},
year = {1975},
pages = { 969-974},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343199}
}
Beran, Rudolf. Tail Probabilities of Noncentral Quadratic Forms. Ann. Statist., Tome 3 (1975) no. 1, pp. 969-974. http://gdmltest.u-ga.fr/item/1176343199/