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Computation of a multivariate $F$ distribution

Authors: D. E. Amos and W. G. Bulgren
Journal: Math. Comp. 26 (1972), 255-264
MSC: Primary 65D20
MathSciNet review: 0298881
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Abstract: Methods for evaluating the joint cumulative probability integral associated with random variables ${F_k} = ({X_k}/{r_k})/(Y/s),k = 1,2, \cdots ,n$, are considered where the ${X_k}$ and $Y$ are independently ${\chi ^2}({r_k})$ and ${\chi ^2}(s)$, respectively. For $n = 2$, series representations in terms of incomplete beta distributions are given, while a quadrature with efficient procedures for the integrand is presented for $n \geqq 2$. The results for $n = 2$ are applied to the evaluation of the correlated bivariate $F$ distribution.

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Keywords: Dirichlet distribution, maximum <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$F$"> distribution, multivariate <IMG WIDTH="22" HEIGHT="23" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="${t^2}$"> distribution, <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img16.gif" ALT="$F$"> with correlation, ranking and selection
Article copyright: © Copyright 1972 American Mathematical Society