Mathematicae Probability and Statistics 22(1,2) (2002) 37-51
EXACT DISTRIBUTION FOR THE GENERALIZED F TESTS
|Miguel Fonseca, Joao Tiago Mexia
Department of Mathematics, Faculty of Science and Technology
New University of Lisbon
Monte da Caparica 2829-516 Caparica, Portugal
Institute of Mathematics, University of Zielona Góra
Podgórna 50 65-246 Zielona Góra, Poland
Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their
degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees
of freedom either in the numerator or in the denominator are even. An example is given to show how these
expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover,
when carrying out adaptative tests, these expressions enable us to estimate the p-values whenever they are
Keywords: exact distribution theory, hypothesis testing, generalized F distribution, adaptative
2000 Mathematics Subject Classification: 62E15, 62H10, 62H15, 62J10.
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Received 15 October 2002