Computation of a multivariate $F$ distribution

Authors:
D. E. Amos and W. G. Bulgren

Journal:
Math. Comp. **26** (1972), 255-264

MSC:
Primary 65D20

DOI:
https://doi.org/10.1090/S0025-5718-1972-0298881-9

MathSciNet review:
0298881

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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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Additional Information

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