On using Newton's method for computing the noncentrality parameter of the noncentral F distribution

Abstract

This article deals with how to enhance computational efficiency of Newton's method for computing the noncentrality parameter of the noncentral F distribution. Some relationship between recurrence formulas for computing the noncentral F distribution function and its derivative with respect to the noncentrality parameter is investigated. Use of the relationship discovered can combine the evaluations of the noncentral F distribution function and its derivative, and therefore can reduce the amount of computations during Newton's process. An efficient algorithm featuring this finding is provided in a step-by-step form.