On the computation of central and noncentral beta probabilities

Carl M.S. Lee

doi:10.1080/00949659208811423

On the computation of central and noncentral beta probabilities

Carl M.S. Lee

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

3 Scopus citations

Abstract

A new method for evaluating the incomplete beta distribution function, I_r(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 language	English
Pages (from-to)	1-10
Number of pages	10
Journal	Journal of Statistical Computation and Simulation
Volume	43
Issue number	1-2
DOIs	https://doi.org/10.1080/00949659208811423
State	Published - Oct 1 1992
Externally published	Yes

Keywords

Algorithm
Hypergeometric Series
Noncentral F
Power Series Expansion
Recursive Formula

Access to Document

10.1080/00949659208811423

Cite this

@article{b80fdb2f13be41adb1b90efaae014574,

title = "On the computation of central and noncentral beta probabilities",

abstract = "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.",

keywords = "Algorithm, Hypergeometric Series, Noncentral F, Power Series Expansion, Recursive Formula",

author = "Lee, {Carl M.S.}",

year = "1992",

month = oct,

day = "1",

doi = "10.1080/00949659208811423",

language = "English",

volume = "43",

pages = "1--10",

journal = "Journal of Statistical Computation and Simulation",

issn = "0094-9655",

publisher = "Journal of Statistical Computation and Simulation",

number = "1-2",

}

TY - JOUR

T1 - On the computation of central and noncentral beta probabilities

AU - Lee, Carl M.S.

PY - 1992/10/1

Y1 - 1992/10/1

N2 - 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.

AB - 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.

KW - Algorithm

KW - Hypergeometric Series

KW - Noncentral F

KW - Power Series Expansion

KW - Recursive Formula

UR - http://www.scopus.com/inward/record.url?scp=21144465233&partnerID=8YFLogxK

U2 - 10.1080/00949659208811423

DO - 10.1080/00949659208811423

M3 - Article

AN - SCOPUS:21144465233

SN - 0094-9655

VL - 43

SP - 1

EP - 10

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

IS - 1-2

ER -

On the computation of central and noncentral beta probabilities

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this