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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Computation of a multivariate $F$ distribution
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by D. E. Amos and W. G. Bulgren PDF
Math. Comp. 26 (1972), 255-264 Request permission


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
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 255-264
  • MSC: Primary 65D20
  • DOI:
  • MathSciNet review: 0298881