On the computation of f-cumulative probabilities

Carl M.S. Lee

doi:10.1080/03610918808812720

On the computation of f-cumulative probabilities

Carl M.S. Lee

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 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 language	English
Pages (from-to)	1191-1201
Number of pages	11
Journal	Communications in Statistics Part B: Simulation and Computation
Volume	17
Issue number	4
DOIs	https://doi.org/10.1080/03610918808812720
State	Published - Jan 1 1988
Externally published	Yes

Keywords

F-distribution
Incomplete beta function
algorithm
recursive formula

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10.1080/03610918808812720

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AB - 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.

KW - F-distribution

KW - Incomplete beta function

KW - algorithm

KW - recursive formula

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SN - 0361-0918

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ER -

On the computation of f-cumulative probabilities

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Keywords

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