Appendix C: References
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Abramowitz, Milton, and Irene A. Stegun (editors) (1964), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Washington.
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Aird, Thomas J., and Byron W. Howell (1991), IMSL Technical Report 9103, IMSL, Houston.
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Akima, H. (1970), A new method of interpolation and smooth curve fitting based on local procedures, Journal of the ACM, 17, 589−602.
Barnett
Barnett, A.R. (1981), An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy, Computer Physics Communication, 21, 297−314.
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Boisvert, Ronald F., Sally E. Howe, David K. Kahaner, and Jeanne L. Springmann (1990), Guide to Available Mathematical Software, NISTIR 90-4237, National Institute of Standards and Technology, Gaithersburg, Maryland.
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Bosten, Nancy E., and E.L. Battiste (1974b), Incomplete beta ratio, Communications of the ACM, 17, 156−157.
Bosten, Nancy E., and E.L. Battiste (1974), Remark on algorithm 179, Communications of the ACM, 17, 153.
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Burgoyne, F.D. (1963), Approximations to Kelvin functions, Mathematics of Computation 83, 295−298.
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Butler, R. W., and M. S. Paolella (1999), Calculating the Density and Distribution Function for the Singly and Doubly Noncentral F, Preliminary Version, Paolella.pdf, p.10, eq.(30) and ff.
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Carlson, B.C. (1979), Computing elliptic integrals by duplication, Numerische Mathematik, 33, 1−16.
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Carlson, B.C., and E.M. Notis (1981), Algorithms for incomplete elliptic integrals, ACM Transactions on Mathematical Software, 7, 398−403.
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Cody, W.J. (1969) Performance testing of function subroutines, Proceedings of the Spring Joint Computer Conference, American Federation for Information Processing Societies Press, Montvale, New Jersey, 759−763.
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Cody et al.
Cody, W.J., R.M. Motley, and L.W. Fullerton (1976), The computation of real fractional order Bessel functions of the second kind, Applied Mathematics Division Technical Memorandum No. 291, Argonne National Laboratory, Argonne.
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Conover, W.J. (1980), Practical Nonparametric Statistics, 2d ed., John Wiley & Sons, New York.
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Cooper, B.E. (1968), Algorithm AS4, An auxiliary function for distribution integrals, Applied Statistics, 17, 190−192.
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Eckhardt, Ulrich (1977), A rational approximation to Weierstrass' P-function. II: The Lemniscatic case, Computing, 18, 341−349.
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Fox, P.A., A.D. Hall, and N.L. Schryer (1978), The PORT mathematical subroutine library, ACM Transactions on Mathematical Software, 4, 104−126.
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Gautschi, Walter (1964), Bessel functions of the first kind, Communications of the ACM, 7, 187−198.
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Gautschi, Walter (1974), Algorithm 471: Exponential integrals, Collected Algorithms from CACM, 471.
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Gautschi, Walter (1979), Algorithm 542: Incomplete gamma functions, ACM Transactions on Mathematical Software, 5, 482−489.
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Hart, John F., E.W. Cheney, Charles L. Lawson, Hans J. Maehly, Charles K. Mesztenyi, John R. Rice, Henry G. Thacher, Jr., and Christoph Witzgall (1968), Computer Approximations, John Wiley & Sons, New York.
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Hill, G.W. (1970), Student's t-distribution, Communications of the ACM, 13, 617−619.
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Hodge, D.B. (1972), The calculation of the eigenvalues and eigenvectors of Mathieu's equation, NASA Contractor Report, The Ohio State University, Columbus, Ohio.
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Hosking, J.R.M., Wallis, J.R., and E.F. Wood. (1985). “Estimation of the Generalized Extreme Value Distribution by the Method of Probability-Weighted Moments.” Technometrics. Vol 27. No. 3. pp 251-261.
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Hosking, J.R.M. and J.R. Wallis. (1987). “Parameter and Quantile Estimation for the Generalized Pareto Distribution.” Technometrics. Vol 29. No. 3. pp 339-349.
IEEE
ANSI/IEEE Std 754-1985 (1985), IEEE Standard for Binary Floating-Point Arithmetic, The IEEE, Inc., New York.
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Johnson, Norman L., and Samuel Kotz (1969), Discrete Distributions, Houghton Mifflin Company, Boston.
Johnson, Norman L., and Samuel Kotz (1970a), Continuous Distributions-1, John Wiley & Sons, New York.
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Kendall, Maurice G., and Alan Stuart (1979), The Advanced Theory of Statistics, Volume 2: Inference and Relationship, 4th ed., Oxford University Press, New York.
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Kim, P.J., and Jennrich, R.I. (1973), Tables of the exact sampling distribution of the two sample Kolmogorov-Smirnov criterion Dmn (m < n), in Selected Tables in Mathematical Statistics, Volume 1, (edited by H.L. Harter and D.B. Owen), American Mathematical Society, Providence, Rhode Island.
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Kinnucan, P., and H. Kuki (1968), A single precision inverse error function subroutine, Computation Center, University of Chicago.
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Luke, Y.L. (1969), The Special Function and their Approximations, Volume 1, Academic Press, 34.
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Majumder , K. L., and G. P. Bhattacharjee (1973), The Incomplete Beta Integral, Algorithm AS 63:Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 3,. 409-411, Blackwell Publishing for the Royal Statistical Society, http://www.jstor.org/stable/2346797.
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Olver, F.W.J., and D.J. Sookne (1972), A note on the backward recurrence algorithms, Mathematics of Computation, 26, 941−947.
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Owen, D.B. (1962), Handbook of Statistical Tables, Addison-Wesley Publishing Company, Reading, Mass.
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Pennisi, L.L. (1963), Elements of Complex Variables, Holt, Rinehart and Winston, New York.
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Skovgaard, Ove (1975), Remark on algorithm 236, ACM Transactions on Mathematical Software, 1, 282−284.
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Sookne, D.J. (1973a), Bessel functions I and J of complex argument and integer order, National Bureau of Standards Journal of Research B, 77B, 111−114.
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Stephens, M.A., and D'Agostino, R.B (1986), Tests based on EDF statistics., Goodness-of-Fit Techniques. Marcel Dekker, New York.
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Strecok, Anthony J. (1968), On the calculation of the inverse of the error function, Mathematics of Computation, 22, 144−158.
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Temme, N. M. (1975), On the numerical evaluation of the modified Bessel function of the third kind, Journal of Computational Physics, 19, 324−337.
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Thompson, I.J. and A.R. Barnett (1987), Modified Bessel functions Iν(z) and Kν(z) of real order and complex argument, to selected accuracy, Computer Physics Communication, 47, 245−257.
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