A Unified Way to Represent and Compute the Cumulative Distribution Function for Noncentral t, F, and χ²

Abstract

This short article shows an unified approach to representing and computing the cumulative distribution function for noncentral t, F, and χ². Unlike the existing algorithms, which involve different expansion and/or recurrence, the new approach consistently represents all the three noncentral cumulative distribution functions as the integral of the normal cumulative distribution function and χ² density function.

Keywords:

• Computing algorithm
• Noncentral F
• Noncentral t
• Noncentral χ²

Mathematics Subject Classification:

• 60E05
• 62E15