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ArticleOriginal scientific text

Title

Exact distribution for the generalized F tests

Authors 1, 1, 2

Affiliations

  1. Department of Mathematics, Faculty of Science and Technology, New University of Lisbon, Monte da Caparica 2829-516 Caparica, Portugal
  2. Institute of Mathematics, University of Zielona Góra, Podgórna 50 65-246 Zielona Góra, Poland

Abstract

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 available.

Keywords

ENG
exact distribution theory, hypothesis testing, generalized F distribution, adaptative test

Bibliography

  1. E. Gasiorek, A. Michalski and R. Zmyślony, Tests of independence of normal random variables with known and unknown variance ratio, Discussiones Mathematicae - Probability and Statistics 2 (2000), 237-247.
  2. A.I. Khuri, T. Matthew and B.K. Sinha, Statistical Tests for Mixed Linear Models, John Wiley & Sons New York 1998.
  3. A. Michalski and R. Zmyślony, Testing hypothesis for variance components in mixed linear models, Statistics 27 (1996), 297-310.
  4. A. Michalski and R. Zmyślony, Testing hypothesis for linear functions of parameters in mixed linear models, Tatra Mt. Math. Pub. 17 (1999), 103-110.
Discussiones Mathematicae Probability and Statistics
2002/22/1-2
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Pages:
37-51
Main language of publication
English
Received
2002-10-15
Published
2002

DOI: 10.7151/dmps.1030

Exact and natural sciences