FNLSpecFunc : Appendix B References
Appendix B References
Abramowitz and Stegun
Abramowitz, Milton, and Irene A. Stegun (editors) (1964), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Washington.
Abramowitz, Milton, and Irene A. Stegun (editors) (1972), Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th Edition, US Government Printing Office, Washington, DC, Chapter 9.
Aird and Howell
Aird, Thomas J., and Byron W. Howell (1991), IMSL Technical Report 9103, IMSL, Houston.
Akima
Akima, H. (1970), A new method of interpolation and smooth curve fitting based on local procedures, Journal of the ACM, 17, 589602.
Barnett
Barnett, A.R. (1981), An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy, Computer Physics Communications, 21, 297314.
Boisvert, Howe, Kahaner, and Springmann
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.
Boisvert, Ronald F., Sally E. Howe, and David K. Kahaner (1985), GAMS: A framework for the management of scientific software, ACM Transactions on Mathematical Software, 11, 313355.
Bosten and Battiste
Bosten, Nancy E., and E.L. Battiste (1974b), Incomplete beta ratio, Communications of the ACM, 17, 156157.
Bosten, Nancy E., and E.L. Battiste (1974), Remark on algorithm 179, Communications of the ACM, 17, 153.
Burgoyne
Burgoyne, F.D. (1963), Approximations to Kelvin functions, Mathematics of Computation 83, 295298.
Butler and Paolella
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.
Carlson
Carlson, B.C. (1979), Computing elliptic integrals by duplication, Numerische Mathematik, 33, 116.
Carlson and Notis
Carlson, B.C., and E.M. Notis (1981), Algorithms for incomplete elliptic integrals, ACM Transactions on Mathematical Software, 7, 398403.
Cody
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, 759763.
Cody, W.J. (1983), Algorithm 597: A sequence of modified Bessel functions of the first kind, ACM Transactions on Mathematical Software, 9, 242245.
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.
Conover
Conover, W.J. (1980), Practical Nonparametric Statistics, 2d ed., John Wiley & Sons, New York.
Cooper
Cooper, B.E. (1968), Algorithm AS4, An auxiliary function for distribution integrals, Applied Statistics, 17, 190192.
Eckhardt
Eckhardt, Ulrich (1977), A rational approximation to Weierstrass’ P‑function. II: The Lemniscatic case, Computing, 18, 341349.
Eckhardt, Ulrich (1980), Algorithm 549: Weierstrass’ elliptic functions, ACM Transactions on Mathematical Software, 6, 112120.
Fabijonas et al.
B. R. Fabijonas, D. W. Lozier, and F. W. J. Olver Computation of Complex Airy Functions and Their Zeros Using Asymptotics and the Differential Equation, ACM Transactions on Mathematical Software, Vol. 30, No. 4, December 2004, 471–490.
Fox et al.
Fox, P.A., A.D. Hall, and N.L. Schryer (1978), The PORT mathematical subroutine library, ACM Transactions on Mathematical Software, 4, 104126.
Gautschi
Gautschi, Walter (1964), Bessel functions of the first kind, Communications of the ACM, 7, 187198.
Gautschi, Walter (1969), Complex error function, Communications of the ACM, 12, 635. Gautschi, Walter (1970), Efficient computation of the complex error function, SIAM Journal on Mathematical Analysis, 7, 187198.
Gautschi, Walter (1974), Algorithm 471: Exponential integrals, Collected Algorithms from CACM, 471.
Gautschi, Walter (1979), A computational procedure for the incomplete gamma function, ACM Transactions on Mathematical Software, 5, 466481.
Gautschi, Walter (1979), Algorithm 542: Incomplete gamma functions, ACM Transactions on Mathematical Software, 5, 482489.
Giles and Feng
Giles, David E. and Hui Feng. (2009).  “Bias‑Corrected Maximum Likelihood Estimation of the Parameters of the Generalized Pareto Distribution.”  Econometrics Working Paper EWP0902, Department of Economics, University of Victoria.
Gradshteyn and Ryzhik
Gradshteyn, I.S. and I.M. Ryzhik (1965), Table of Integrals, Series, and Products, (translated by Scripta Technica, Inc.), Academic Press, New York.
Hart et al.
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.
Hill
Hill, G.W. (1970), Student’s t‑distribution, Communications of the ACM, 13, 617619.
Hodge
Hodge, D.B. (1972), The calculation of the eigenvalues and eigenvectors of Mathieu’s equation, NASA Contractor Report, The Ohio State University, Columbus, Ohio.
Hosking, et al.
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.
Hosking and Wallis
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.
Johnson and Kotz
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.
Johnson, Norman L., and Samuel Kotz (1970b), Continuous Distributions‑2, John Wiley & Sons, New York.
Kendall and Stuart
Kendall, Maurice G., and Alan Stuart (1979), The Advanced Theory of Statistics, Volume 2: Inference and Relationship, 4th ed., Oxford University Press, New York.
Kim and Jennrich
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.
Kinnucan and Kuki
Kinnucan, P., and H. Kuki (1968), A single precision inverse error function subroutine, Computation Center, University of Chicago.
Luke
Luke, Y.L. (1969), The Special Function and their Approximations, Volume 1, Academic Press, 34.
Majumder and Bhattacharjee
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.
NATS FUNPACK
NATS (National Activity to Test Software) FUNPACK (1976), Argonne National Laboratory, Argonne Code Center, Argonne.
Olver and Sookne
Olver, F.W.J., and D.J. Sookne (1972), A note on the backward recurrence algorithms, Mathematics of Computation, 26, 941947.
Owen
Owen, D.B. (1962), Handbook of Statistical Tables, Addison‑Wesley Publishing Company, Reading, Mass.
Owen, D.B. (1965), A special case of the bivariate non‑central t‑distribution, Biometrika, 52, 437446.
Pennisi
Pennisi, L.L. (1963), Elements of Complex Variables, Holt, Rinehart and Winston, New York.
Skovgaard
Skovgaard, Ove (1975), Remark on algorithm 236, ACM Transactions on Mathematical Software, 1, 282284.
Sookne
Sookne, D.J. (1973a), Bessel functions I and J of complex argument and integer order, National Bureau of Standards Journal of Research B, 77B, 111114.
Sookne, D.J. (1973b), Bessel functions of real argument and integer order, National Bureau of Standards Journal of Research B, 77A, 125132.
Stephens
Stephens, M.A., and D’Agostino, R.B (1986), Tests based on EDF statistics., Goodness‑of‑Fit Techniques. Marcel Dekker, New York.
Strecok
Strecok, Anthony J. (1968), On the calculation of the inverse of the error function, Mathematics of Computation, 22, 144158.
Temme
Temme, N. M. (1975), On the numerical evaluation of the modified Bessel function of the third kind, Journal of Computational Physics, 19, 324337.
Thompson and Barnett
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 Communications, 47, 245257.
Yousif and Melka
Yousif, Hashim A., and Richard Melka (1997), Bessel function of the first kind with complex argument, Computer Physics Communications, vol. 106, no. 3, 199206.
Yousif, Hashim A., and Richard Melka (2003), Computing Bessel functions of the second kind in extreme parameter regimes, Computer Physics Communications, 151, 2534.