Algorithm 708: Significant digit computation of the incomplete beta function ratios

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Algorithm 708: Significant digit computation of the incomplete beta function ratios

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ACM Transactions on Mathematical Software (TOMS) archive
Volume 18 , Issue 3 (September 1992) table of contents

Pages: 360 - 373

Year of Publication: 1992

ISSN:0098-3500

Authors

Armido R. Didonato	U.S. Naval Surface Warfare Center
Alfred H. Morris, Jr.	U.S. Naval Surface Warfare Center

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 11, Downloads (12 Months): 123, Citation Count: 5

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appendices and supplements abstract references cited by index terms collaborative colleagues

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APPENDICES and SUPPLEMENTS

BRATIO (708.gz) (15 KB)

incomplete Beta function IX(a,b)
Gams: c7

ABSTRACT

An algorithm is given for evaluating the incomplete beta function ratio Ix(a,b) and its complement 1 - Ix(a,b). A new continued fraction and a new asymptotic series are used with classical results. A transportable Fortran subroutine based on this algorithm is currently in use. It is accurate to 14 significant digits when precision is not restricted by inherent error.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	ABRAMOWiTZ, M., AND 8TEGUN, I., Ed~. Hq, ndbook ofMathemc~tical Ft~nctions. Dover, New York, 1965.
	2	A~os, D. E., AND DANIEL S L. Significant digit incomplete beta ratios Rep. SC-DR-69-591, Sandia Laboratories, Albuquerque, N.M., 1969.
	3	AROIAN, L.A. Continued fractions for the incomplete beta function. Am. Math. Stat. 12 (1941), 218 223.
	4	Armido R DiDonato , Alfred H Morris, Jr., Computation of the incomplete gamma function ratios and their inverse, ACM Transactions on Mathematical Software (TOMS), v.12 n.4, p.377-393, Dec. 1986 [doi>10.1145/22721.23109]
	5	DIDONATO, A. R., AND MORRIS, A.H. Significant digit computation of the incomplete beta function ratios. Rep. NSWC TR 88-365, Naval Surface Warfare Center, Dahlgren, Va., 1988.
	6	HENRICI, P. Applied and Computational Complex Analysis (Vol. 1). Wiley, New York, 1974.
	7	MORRIS, A. It. NSWC library of mathematical subroutines. Rep. NSWC TR 90-21, Naval Surface Warfare Center, Dahlgren, Va., 1990.
	8	POUR^HMADI, M. Taylor expansion of exp(Y~_0 akzk) and some applications. Am. Math. Mon. (1984), 303 307.
	9	TRETTER, M. J., AND WALSTER, G.W. Continued fractions for the incomplete beta function: Additions and corrections. Ann. Stat. 7 (1979), 462-465.
	10	WALL, H.S. Analytic Theory of Continued Fractions. Van Nostrand, New York, 1948.
	11	WISE, M.E. The incomplete beta function as a contour integral and a quickly converging series for its inverse. Blometrika 37 (1950), 208-218.

CITED BY 5

	David M. Smith, Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions, ACM Transactions on Mathematical Software (TOMS), v.27 n.4, p.377-387, December 2001
	Barry W. Brown , Lawrence B. Levy , James Lovato , Kathy Russell , Floyd M. Spears, Algorithm 762; LLDRLF, log-likelihood and some derivatives for log-F models, ACM Transactions on Mathematical Software (TOMS), v.22 n.3, p.372-382, Sept. 1996
	Barry W. Brown , Lawrence B. Levy, Certification of Algorithm 708: significant-digit computation of the incomplete beta, ACM Transactions on Mathematical Software (TOMS), v.20 n.3, p.393-397, Sept. 1994
	Pierre L'ecuyer , Richard Simard, Inverting the symmetrical beta distribution, ACM Transactions on Mathematical Software (TOMS), v.32 n.4, p.509-520, December 2006
	Kevin Beyer , Peter J. Haas , Berthold Reinwald , Yannis Sismanis , Rainer Gemulla, On synopses for distinct-value estimation under multiset operations, Proceedings of the 2007 ACM SIGMOD international conference on Management of data, June 11-14, 2007, Beijing, China