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Numerical Evaluation of Special Functions
D. W. Lozier and F. W. J. Olver
5.6. Incomplete Bessel Functions, Incomplete Beta Function
.
This section includes F--, t-- and von Mises' distribution functions.
5.6.1. Incomplete Bessel Functions.
Software Packages:
[ Hil77, Fortran]
.
5.6.2. Incomplete Beta Function.
Software Packages:
[ DM92, Fortran]
,
[ Dor68, Algol]
,
[ Gau64, Algol]
,
[ Hil70a, Algol]
,
[ Lev69, Fortran]
,
[ MB73a, Fortran]
,
[ Mor69, Algol]
,
[ Phi90, Basic]
.
Intermediate Libraries:
[ Bak92]
,
[ Mos89]
,
[ ULI90]
.
Comprehensive Libraries:
IMSL,
NAG,
Numerical Recipes,
Scientific Desk,
SLATEC.
Interactive Systems:
Mathematica.
5.6.3. Inverse Incomplete Beta Function.
Algorithms:
[ MB73b]
.
Software Packages:
[ AS93a, Fortran]
,
[ Hil70b, Algol]
.
Intermediate Libraries:
[ Mos89]
,
[ ULI90]
.
Comprehensive Libraries:
IMSL,
NAG,
Scientific Desk.
Interactive Systems:
Maple,
Mathematica.
5.6.4. Articles.
[ AS93b]
,
[ DJ67]
,
[ OM68]
,
[ Tem92b]
.
References
- AS93a
-
R. W. Abernathy and R. P. Smith, Algorithm 724. Program to calculate
F--percentiles, ACM Trans. Math. Software 19 (1993), 481--483.
- AS93b
-
R. W. Abernathy and R. P. Smith, Applying series expansion to the inverse
beta distribution to find percentiles of the F--distribution, ACM Trans.
Math. Software 19 (1993), 474--480.
- Bak92
-
L. Baker, C mathematical function handbook, McGraw-Hill, Inc., New
York, 1992, includes diskette.
- DJ67
-
A. R. DiDonato and M. P. Jarnagin, The efficient calculation of the
incomplete beta-function ratio for half-integer values of the parameters
a,b, Math. Comp. 21 (1967), 652--662.
- DM92
-
A. R. DiDonato and A. H. Morris, Jr., Algorithm 708. Significant digit
computation of the incomplete beta function ratios, ACM Trans. Math.
Software 18 (1992), 360--373.
- Dor68
-
E. Dorrer, Algorithm 322. F--distribution, Comm. ACM 11 (1968),
116--117, for certification see same journal v. 12 (1969), p. 39.
- Gau64
-
W. Gautschi, Algorithm 222. Incomplete beta function ratios, Comm. ACM
7 (1964), 143--144, for certification see same journal v. 7 (1964), p.
244.
- Hil70a
-
G. W. Hill, Algorithm 395. Student's t--distribution, Comm. ACM
13 (1970), 617--619, for remarks see ACM Trans. Math. Software v. 5 (1979),
pp. 238--239, v. 7 (1981), pp. 247--249.
- Hil70b
-
G. W. Hill, Algorithm 396. Student's t--quantiles, Comm. ACM 13
(1970), 619--620, for remarks see ACM Trans. Math. Software v. 5 (1979), pp.
238--239, v. 7 (1981), pp. 250--251.
- Hil77
-
G. W. Hill, Algorithm 518. Incomplete Bessel function :
The von Mises distribution, ACM Trans. Math. Software 3 (1977),
279--284.
- Lev69
-
D. A. Levine, Algorithm 344. Student's t--distribution, Comm. ACM
12 (1969), 37--38, for remarks see same journal v. 13 (1970), pp. 124
and 449.
- MB73a
-
K. L. Majumder and G. P. Bhattacharjee, Algorithm AS 63. The
incomplete beta integral, Appl. Statist. 22 (1973), 409--411, for
remark see same journal v. 26 (1977), pp. 111--114.
- MB73b
-
K. L. Majumder and G. P. Bhattacharjee, Algorithm AS 64. Inverse of
the incomplete beta function ratio, Appl. Statist. 22 (1973),
411--414, for remarks and corrections see same journal v. 26 (1977), pp.
111--114, v. 39 (1990), pp. 309--310, v. 40 (1991), p. 236.
- Mor69
-
J. Morris, Algorithm 346. F--test probabilities, Comm. ACM 12
(1969), 184--185, for remark see ACM Trans. Math. Software v. 14 (1988), pp.
288--289.
- Mos89
-
S. L. B. Moshier, Methods and programs for mathematical functions, Ellis
Horwood Limited, Chichester, 1989, separate diskette.
- OM68
-
D. Osborn and R. Madey, The incomplete beta function and its ratio to the
complete beta function, Math. Comp. 22 (1968), 159--162.
- Phi90
-
H. N. Phien, A note on the computation of the incomplete beta function,
Adv. Engrg. Software 12 (1990), 39--44.
- Tem92
-
N. M. Temme, Asymptotic inversion of the incomplete beta function, J.
Comput. Appl. Math. 41 (1992), 145--157.
- ULI90
-
Mathematical function library for Microsoft--C, United Laboratories,
Inc., John Wiley & Sons, 1990, includes diskettes. Edition also
exists in Fortran (1989).
Abstract:
This document is an excerpt from the current hypertext version of
an article that appeared in Walter Gautschi (ed.),
Mathematics of Computation 1943--1993: A Half-Century of
Computational Mathematics, Proceedings of Symposia in
Applied Mathematics 48, American Mathematical Society,
Providence, RI 02940, 1994.
The symposium was held at the University of British Columbia
August 9--13, 1993, in honor of the fiftieth anniversary of
the journal Mathematics of Computation.
The original abstract follows.
Higher transcendental functions continue to play varied and
important roles in investigations by engineers, mathematicians,
scientists and statisticians.
The purpose of this paper is to assist in locating useful approximations
and software for the numerical generation of these functions, and to
offer some suggestions for future developments in this field.
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, Md 20899
E-mail address: dlozier@nist.gov
Institute for Physical Science and Technology,
University of Maryland,
College Park, MD 20742
E-mail address: olver@bessel.umd.edu
The research of the second author has been supported by NSF
Grant CCR 89-14933.
1991 Mathematics Subject Classification. Primary 65D20;
Secondary 33-00.
Daniel W Lozier
Fri Apr 7 14:14:39 EDT 1995