On the computation of central and noncentral beta probabilities

Carl M.S. Lee

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A new method for evaluating the incomplete beta distribution function, Ir(p, q), is presented in this article. This method reduces both parameters simultaneously. A comparison on the IBM 3090 VM/CMS is made to compare the new approach with the one by Bosten and Battiste (1974), which is currently used by IMSL (IMSL, 1987). Results show that the absolute difference is at most 10−7 in double precision. For the comparison of cpu time, the new approach is twice as fast for (p, q) within 200, and about 10 to 50% faster for (p, q) between 200 and 300. Comparison is also made when the IBM optimization complier option is applied. It appears that this new approach performs consistently better for (p, q) less than 500 and the values of x from 0 to 1. Finally, some computational aspects are discussed for evaluating noncentral beta and noncentral F probabilities.

Original languageEnglish
Pages (from-to)1-10
Number of pages10
JournalJournal of Statistical Computation and Simulation
Issue number1-2
StatePublished - Oct 1 1992
Externally publishedYes


  • Algorithm
  • Hypergeometric Series
  • Noncentral F
  • Power Series Expansion
  • Recursive Formula


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