The quotient of two linear combinations of independent chi-squares will have a generalized F distribution. Exact expressions for these distributions when the chi-square are central and those in the numerator or in the denominator have even degrees of freedom were given in Fonseca et al. (2002). These expressions are now extended for non-central chi-squares. The case of random non-centrality parameters is also considered.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1074,
author = {C\'elia Nunes and Jo\~ao Tiago Mexia},
title = {Non-central generalized F distributions},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {26},
year = {2006},
pages = {47-61},
zbl = {1128.62018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1074}
}
Célia Nunes; João Tiago Mexia. Non-central generalized F distributions. Discussiones Mathematicae Probability and Statistics, Tome 26 (2006) pp. 47-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1074/
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