Self-validated computations for the probabilities of the central bivariate chi-square distribution and a bivariate F distribution
Self-validated computations using interval analysis produce results with a guaranteed error bound. This article presents methods for self-validated computation of probabilities and percentile points of the bivariate chi-square distribution and a bivariate F distribution. For the computation of critical points (c(1), c(2)) in the equation P(Y-1 less than or equal to c(1), Y-2 less than or equal to c(2)) = 1 - alpha, the case c(1) = c(2) is considered. A combination of interval secant and bisection algorithms is developed for finding enclosures of the percentile points of the distribution. Results are compared to previously published tables.
interval analysis guaranteed error bound secant search