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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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

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
  • © Copyright 1972 American Mathematical Society
  • Journal: Math. Comp. 26 (1972), 255-264
  • MSC: Primary 65D20
  • DOI: https://doi.org/10.1090/S0025-5718-1972-0298881-9
  • MathSciNet review: 0298881