Geodesic
Non-central generalized F distributions
Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 1, pp. 47-61.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: exact distributions, random non-centrality parameters, generalized F distributions 
@article{DMPS_2006_26_1_a2,
     author = {Nunes, C\'elia and Mexia, Jo\~ao},
     title = {Non-central generalized {F} distributions},
     journal = {Discussiones Mathematicae. Probability and Statistics},
     pages = {47--61},
     publisher = {mathdoc},
     volume = {26},
     number = {1},
     year = {2006},
     zbl = {1128.62018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a2/}
}
TY  - JOUR
AU  - Nunes, Célia
AU  - Mexia, João
TI  - Non-central generalized F distributions
JO  - Discussiones Mathematicae. Probability and Statistics
PY  - 2006
SP  - 47
EP  - 61
VL  - 26
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a2/
LA  - en
ID  - DMPS_2006_26_1_a2
ER  - 
%0 Journal Article
%A Nunes, Célia
%A Mexia, João
%T Non-central generalized F distributions
%J Discussiones Mathematicae. Probability and Statistics
%D 2006
%P 47-61
%V 26
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a2/
%G en
%F DMPS_2006_26_1_a2
Nunes, Célia; Mexia, João. Non-central generalized F distributions. Discussiones Mathematicae. Probability and Statistics, Tome 26 (2006) no. 1, pp. 47-61. http://geodesic.mathdoc.fr/item/DMPS_2006_26_1_a2/

[1] R.B. Davies, Algorithm AS 155: The distribution of a linear combinations of χ² random variables, Applied Statistics 29 (1980), 232-333.

[2] J.P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika 48 (1961), 419-426.

[3] M. Fonseca, J.T. Mexia and R. Zmyślony, Exact distribution for the generalized F tests, Discussiones Mathematicae Probability and Statistics 22 (2002), 37-51.

[4] D.W. Gaylor and F.N. Hopper, Estimating the degrees of freedom for linear combinations of mean squares by Satterthwaite's formula, Technometrics 11 (1969), 691-706.

[5] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.

[6] A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mountain Mathematical Publications 17 (1999), 103-110.

[7] H. Robbins, Mixture of distribution, The Annals of Mathematical Statistics 19 (1948), 360-369.

[8] H. Robbins and E.J.G. Pitman, Application of the method of mixtures to quadratic forms in normal variates, The Annals of Mathematical Statistics 20 (1949), 552-560.

[9] F.E. Satterthwaite, An approximate distribution of estimates of variance components, Biometrics Bulletin 2 (1946), 110-114.