The efficient calculation of the incomplete beta-function ratio for half-integer values of the parameters

Authors:
A. R. DiDonato and M. P. Jarnagin

Journal:
Math. Comp. **21** (1967), 652-662

MSC:
Primary 65.20

DOI:
https://doi.org/10.1090/S0025-5718-1967-0221730-X

MathSciNet review:
0221730

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References | Similar Articles | Additional Information

**[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****[2]**Harald Cramér,*Mathematical Methods of Statistics*, Princeton Mathematical Series, vol. 9, Princeton University Press, Princeton, N. J., 1946. MR**0016588****[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****[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****[7]**O. Ludwig, "Incomplete beta ratio,"*Comm. ACM*, v. 6, 1963, p. 314.**[8]**E. C. Molina, "Expansions for Laplacian integrals of the form ,"*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****[10]**H. E. Soper,*The Numerical Evaluation of the Incomplete B-Function or of the Integral 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**, https://doi.org/10.2307/2332208**[13]**Francesco Giacomo Tricomi,*Differential equations*, Translated by Elizabeth A. McHarg, Hafner Publishing Co., New York, 1961. MR**0138812****[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**, https://doi.org/10.1093/biomet/37.3-4.208**[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****[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****[17]**J. Wishart, "Determination of for large values of , 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****[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**

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DOI:
https://doi.org/10.1090/S0025-5718-1967-0221730-X

Article copyright:
© Copyright 1967
American Mathematical Society