## 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.## References

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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