Non-central generalized F distributions

Célia Nunes; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2006)

  • Volume: 26, Issue: 1, page 47-61
  • ISSN: 1509-9423

Abstract

top
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.

How to cite

top

Célia Nunes, and João Tiago Mexia. "Non-central generalized F distributions." Discussiones Mathematicae Probability and Statistics 26.1 (2006): 47-61. <http://eudml.org/doc/277032>.

@article{CéliaNunes2006,
abstract = {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.},
author = {Célia Nunes, João Tiago Mexia},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {exact distributions; random non-centrality parameters; generalized F distributions; non-centrality parameters},
language = {eng},
number = {1},
pages = {47-61},
title = {Non-central generalized F distributions},
url = {http://eudml.org/doc/277032},
volume = {26},
year = {2006},
}

TY - JOUR
AU - Célia Nunes
AU - João Tiago Mexia
TI - Non-central generalized F distributions
JO - Discussiones Mathematicae Probability and Statistics
PY - 2006
VL - 26
IS - 1
SP - 47
EP - 61
AB - 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.
LA - eng
KW - exact distributions; random non-centrality parameters; generalized F distributions; non-centrality parameters
UR - http://eudml.org/doc/277032
ER -

References

top
  1. [1] R.B. Davies, Algorithm AS 155: The distribution of a linear combinations of χ² random variables, Applied Statistics 29 (1980), 232-333. Zbl0473.62025
  2. [2] J.P. Imhof, Computing the distribution of quadratic forms in normal variables, Biometrika 48 (1961), 419-426. Zbl0136.41103
  3. [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. Zbl1037.62004
  4. [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. [5] A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310. Zbl0842.62059
  6. [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. Zbl0987.62012
  7. [7] H. Robbins, Mixture of distribution, The Annals of Mathematical Statistics 19 (1948), 360-369. Zbl0037.36301
  8. [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. Zbl0036.20801
  9. [9] F.E. Satterthwaite, An approximate distribution of estimates of variance components, Biometrics Bulletin 2 (1946), 110-114. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.