Self-validated Computations for the Probabilities of the Central Bivariate Chi-square Distribution and a Bivariate F Distribution. This work partially supported by National Science Foundation grant DMS-9500831
Kevin Wright, William James Kennedy · Journal of Statistical Computation and Simulation · 2002
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 @ c 1, Y 2 ≤ c 2) = 1 − α, 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.