An Improved Algorithm for Generation of Truncated Normal Distributed Random Numbers
Keywords:
Random numbers generation, Truncated normal distribution, Error function, Inverse error functionAbstract
In this paper we discuss the computational problems of random numbers generation distributed by truncated normal distribution. It is shown that the standard methods and libraries have a limit for truncation point caused by the limit on the smallest number representable by double precision format. Theoretically the problems arise starting from the truncation point ≈ 40, but in practical calculations the limit is lower, starting from ≈ 8.5. An improved method is represented, based on the combination of two approximation algorithms, which with the represented coefficients has 4.5 times more coverage interval than the standard methods.
References
W. H. Press, S. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes: The Art of Scientific Computing, Third Edition, New York, 2007.
L. Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986.
American National Standards Institute and Institute of Electrical and Electronic Engineers, Standard for Binary Floating-Point Arithmetic, ANSI/IEEE Standard 754-1985, 1985.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series - 55, New York, 1964.
F. W. J. Olver, D. W. Lozier, R. F. Boisvert and C. W. Clark, “Error Functions, Dawsons and Fresnel Integrals" NIST Handbook of Mathematical Functions, Cambridge University Press, p. 166, New York, 2010
S. L. Moshier, Cephes Math Library. [Online]. Available: http://www.netlib.org/cephes
J. F. Hart, et al., Computer Approximations, The Siam Series in Applied Mathematics, New York, 1968
W. J. Cody, “Rational Chebyshev approximations for the error function" Math. Comp., vol. 23, pp. 631-637, 1969
GNU Project, GNU Scientific Library. [Online]. Available: https://www.gnu.org/software/gsl/
J. von Neumann, “Various techniques used in connection with random digits. Monte Carlo methods", Nat. Bureau Standards, vol. 12, pp. 36-38, 1951.
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