Statistics and Computing

, Volume 12, Issue 1, pp 9–16

# Calculating the density and distribution function for the singly and doubly noncentral F

• Ronald W. Butler
• Marc S. Paolella
Article

## Abstract

Simple, closed form saddlepoint approximations for the distribution and density of the singly and doubly noncentral F distributions are presented. Their overwhelming accuracy is demonstrated numerically using a variety of parameter values. The approximations are shown to be uniform in the right tail and the associated limitating relative error is derived. Difficulties associated with some algorithms used for “exact” computation of the singly noncentral F are noted.

design of experiments noncentral F saddlepoint approximation statistical computing

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