An F Approximation to the Distribution of a Linear Combination of Chi-squared Variables. |
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Authors: | Andrew T. A. Wood |
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Affiliation: | Division of Public Health , University of Western Australia , 6009 , Nedlands , W.A , QEII |
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Abstract: | A three-parameter F approximation to the distribution of a positive linear combination of central chi-squared variables is described. It is about as easy to implement as the Satterthwaite-Welsh and Hall-Buckley-Eagleson approximations. Some reassuring properties of the F approximation are derived, and numerical results are presented. The numerical results indicate that the new approximation is superior to the Satterthwaite approximation and, for some purposes, better than the Hall-Buckley-Eagleson approximation. It is not quite as good as the Gamma-Weibull approximation due to Solomon and Stephens, but is easier to implement because iterative methods are not required. |
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Keywords: | chi-squared cumulant F distribution inequality moment Satterthwaite-Welsh approximation |
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