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Algorithms for the Beta Distribution Function

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COMPSTAT

Summary

The present paper provides a set of useful algorithms for evaluating the beta distribution function in easily programmed form. These algorithms are the most important of the currently available procedures. Each is expressed in recursive form and a discussion of the quality of each is included. Applications of these algorithms to the evaluation of t, F and noncentral F distribution functions is also included.

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References

  • Abramowitz, M. and Stegun, I.A. (1964) Handbook of Mathematical Functions. National Bureau of Standards, Applied Math. Series, U.S. Govt. Printing Office, Wash. D.C.

    Google Scholar 

  • Aroian, L.A. (1941) Continued Fractions for the Incomplete Beta Function. Annals Math. Statist., 12, 212–223.

    Google Scholar 

  • Aroian, L.A. (1959) Corrections to “Continued Fractions for the Incomplete Beta Function.” Annals Math. Statist. 30, 1265

    Article  Google Scholar 

  • Bargmann, R. E.and Ghosh S. P. (1963) Statistical Distribution Programs for a Computer Language. IBM Watson Research Center Report RC-1094.

    Google Scholar 

  • Boardman,T. J. and Kopitzke, R. W. (1975) Probability and Table Values for Statistical Distributions. Proc. Statist. Comput. Section, Amer. Statist. Assoc, Washington D.C.

    Google Scholar 

  • Bosten, N.E. and Battiste, E.L. (1974) Remark on Algorithm 179 (S14); Incomplete Beta Ratio. Commun. Assoc. Comput. Machin. 17, 156–157.

    Google Scholar 

  • Bouver, H. and Bargmann, R.E. (1975) Computer Algorithm and Modules for The Evaluation of Statistical Distribution Functions. Tech. Report 110, Statistics Dept., Univ. of Georgia, Athens Ga. U.S.A.

    Google Scholar 

  • Johnson, N.L. and Kotz, S. (1970) Continuous Univariate Distributions, vol. 2, Houghton and Mifflin Co. New York.

    Google Scholar 

  • Kennedy, W.J. and Gentle, J. E. (1980) Statistical Computing. New York: Marcel Dekker, Inc.

    Google Scholar 

  • Muller, J.H. (1931) On the Application of Continued Fractions to the Evaluation of Certain Integrals, Biometrika 22, 284–297.

    Google Scholar 

  • Pike, M.C. and Hill, I. D. (1967) Remark on Algorithm 179: Incomplete Beta Ratio, Comm. Assoc. Comp. Machin. 10, 375–376.

    Google Scholar 

  • Pike, M.C., and SooHoo, J. S. (1976) Remark on Algorithm 179: Incomplete Beta Ratio. Trans. Math. Software 2, 201–208.

    Article  Google Scholar 

  • Posten, H.O. (1982) Computer Algorithms for the Classical Distribution Functions. Proc. First Internat. Conf. on Teaching Statistics. Univ. of Sheffield, England, 313–330.

    Google Scholar 

  • Tretter, M.J. and Walster, G. W. (1979) Continued Fractions for the Incomplete Beta Function: Additions and Corrections. Annals Statist. 7, 462–465.

    Article  Google Scholar 

  • Woods, J.D. and Posten, H. O. (1977) The Use of Fourier Series in the Evaluation of Probability Distribution Functions. Commun. Statistics B6, 201–219.

    Google Scholar 

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© 1986 Physica-Verlag, Heidelberg for IASC (International Association for Statistical Computing)

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Posten, H.O. (1986). Algorithms for the Beta Distribution Function. In: De Antoni, F., Lauro, N., Rizzi, A. (eds) COMPSTAT. Physica-Verlag HD. https://doi.org/10.1007/978-3-642-46890-2_46

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  • DOI: https://doi.org/10.1007/978-3-642-46890-2_46

  • Publisher Name: Physica-Verlag HD

  • Print ISBN: 978-3-7908-0355-6

  • Online ISBN: 978-3-642-46890-2

  • eBook Packages: Springer Book Archive

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