Non-central generalized F distributions

• Autorzy: Célia Nunes , João Tiago Mexia
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

exact distributions; random non-centrality parameters; generalized F distributions

Kategorie tematyczne

• 62H10: Distribution of statistics
• 62J99: None of the above, but in this section
• 62J12: Generalized linear models

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae Probability and Statistics
• Rocznik: 2006
• Tom: 26
• Numer: 1
• Strony: 47-61

Daty

wydano

2006

poprawiono

2006-03-14

otrzymano

2006-09-09

Twórcy

autor

Célia Nunes

• Departamento de Matemática da Faculdade de Ciências e Tecnologia Quinta da Torre, 2825-114 Monte de Caparica, Portugal

autor

João Tiago Mexia

• Universidade Nova de Lisboa, Departamento de Matemática da Faculdade de Ciências e Tecnologia Quinta da Torre, 2825-114 Monte da Caparica, Portugal

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmps.1074