On the computation of f-cumulative probabilities

Carl M.S. Lee

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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 l = m, n = 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.

Original languageEnglish
Pages (from-to)1191-1201
Number of pages11
JournalCommunications in Statistics Part B: Simulation and Computation
Issue number4
StatePublished - Jan 1 1988
Externally publishedYes


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


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