Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


The efficient calculation of the incomplete beta-function ratio for half-integer values of the parameters $ a,\,b$

Authors: A. R. DiDonato and M. P. Jarnagin
Journal: Math. Comp. 21 (1967), 652-662
MSC: Primary 65.20
MathSciNet review: 0221730
Full-text PDF Free Access

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] Milton Abramowitz and Irene A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964. MR 0167642 (29 #4914)
  • [2] Harald Cramér, Mathematical Methods of Statistics, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR 0016588 (8,39f)
  • [3] A. R. DiDonato & M. P. Jarnagin, "A method for computing the incomplete beta function ratio," NWL Report 1949 (revised), U. S. Naval Weapons Lab., Dahlgren, Virginia, 1966.
  • [4] Henry E. Fettis, On the calculation of integrals of the form ∫^{𝜃}₀sin^{𝑝}𝜑cos^{𝑞}𝜑𝑑𝜑, J. Math. Physics 33 (1954), 283–289. MR 0064484 (16,289d)
  • [5] W. Gautschi, "Incomplete beta function ratios," Comm. ACM, v. 7, 1964, p. 143.
  • [6] F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956. MR 0075670 (17,788d)
  • [7] O. Ludwig, "Incomplete beta ratio," Comm. ACM, v. 6, 1963, p. 314.
  • [8] E. C. Molina, "Expansions for Laplacian integrals of the form $ \smallint _{{x_1}}^{{x_2}}{[y(t)]^\theta }\Phi (t)dt$," Bell. System Tech. J., v. 11, 1932, p. 563.
  • [9] Tables of the incomplete beta-function, Originally prepared under the direction of and edited by Karl Pearson. Second edition with a new introduction by E. S. Pearson and N. L. Johnson, Published for the Biometrika Trustees at the Cambridge University Press, London, 1968. MR 0226815 (37 #2402)
  • [10] H. E. Soper, The Numerical Evaluation of the Incomplete B-Function or of the Integral $ \smallint _0^x{x^{p - 1}}{(1 - x)^{q - 1}}dx$ for Ranges of x Between 0 and 1, Tracts for Computers, No. VII, Cambridge Univ. Press, New York, 1921.
  • [11] I. C. Tang, "On the computation of a certain type of incomplete beta functions," Comm. ACM, v. 6, 1963, p. 689.
  • [12] Catherine M. Thompson, Tables of percentage points of the incomplete beta-function, Biometrika 32 (1941), 151–181. Prefatory note by E. S. Pearson; description of the calculation by L. J. Comrie and H. O. Hartley; methods of interpolation by H. O. Hartley. MR 0005429 (3,153a)
  • [13] Francesco Giacomo Tricomi, Differential equations, Translated by Elizabeth A. McHarg, Hafner Publishing Co., New York, 1961. MR 0138812 (25 #2254b)
  • [14] M. E. Wise, The incomplete beta function as a contour integral and a quickly converging series for its inverse, Biometrika 37 (1950), 208–218. MR 0040622 (12,724e)
  • [15] M. E. Wise, The incomplete beta function and the incomplete gamma function: An acknowledgment, J. Roy. Statist. Soc. Ser. B. 10 (1948), 264. MR 0028475 (10,453c)
  • [16] M. E. Wise, The use of the negative binomial distribution in an industrial sampling problem, Suppl. J. Roy. Statist. Soc. 8 (1946), 202–211. MR 0021289 (9,49c)
  • [17] J. Wishart, "Determination of $ \smallint _0^\theta {\cos ^{n + 1}}\theta d\theta $ for large values of $ n$, and its application to the probability integral of symmetrical frequency curves," Biometrika, v. 17, 1925, pp. 68, 469.
  • [18] Tables of the cumulative binomial probability distribution, The Annals of the Computation Laboratory of Harvard University, vol. 35, Harvard University Press, Cambridge, Mass., 1955. MR 0082203 (18,517c)
  • [19] Tables of the Binomial Probability Distribution, National Bureau of Standards, Applied Mathematics Series, No. 6, United States Government Printing Office, Washington, D. C., 1950. MR 0035108 (11,692c)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65.20

Retrieve articles in all journals with MSC: 65.20

Additional Information

PII: S 0025-5718(1967)0221730-X
Article copyright: © Copyright 1967 American Mathematical Society