On the computation of F-cumulative probabilities

Abstract

A recursive formula for evaluating incomplete beta integral is obtained by reducing both parameters simultaneously. Applying this identity, we derive an exact expression for F-cumulative probabilities. An algorithm is then derived by using this expression. Results from a single-precision FORTRAN program by using this algorithm are compared with that using MDFD subroutine of IMSL in both of accuracy and speed for degrees of freedom 1 lsequal; m, n $lsequal; 500. It is seen that both results coincide with at least 11 significant digits, and the new algorithm is consistently faster than MDFD by 10 to 15 percent.

Keywords:

• F-distribution
• algorithm
• recursive formula
• Incomplete beta function