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Random variate generation in one line of code

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Published:08 November 1996Publication History

ABSTRACT

A random variate with a given non-uniform distribution can often by generated in one assignment statement if a uniform source and some simple functions are available. We review such one-line methods for most of the key distributions.

References

  1. R. W. Bailey, "Polar generation of random variates with the t distribution," Mathematics of Computation, vol. 62, pp. 779-781, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. D. J. Best, "A simple algorithm for the computer generation of random samples from a Student's t or symmetric beta distribution," in: COMP- STAT 1978: Proceedings in Computational Statistics, ed. L. C. A. Corsten and J. Hermans, pp. 341- 347, Physica Verlag, Wien, Austria, 1978.Google ScholarGoogle Scholar
  3. I. W. Burr, "Cumulative frequency functions," Annals of Mathematical Statistics, vol. 13;, pp. 215- 232, 1942.Google ScholarGoogle ScholarCross RefCross Ref
  4. J. M. Chambers, C. L. Mallows, and B. W. Stuck, "A method for simulating stable random variables," Journal of the American Statistical Association, vol. 71, pp. 340-344, 1976.Google ScholarGoogle ScholarCross RefCross Ref
  5. L. Devroye, Non-Uniform Random Variate Generation, Springer-Verlag, New York, 1986.Google ScholarGoogle Scholar
  6. L. Devroye, "A note on Linnik's distribution," Statistics and Probability Letters, vol. 9, pp. 305-306, 1990.Google ScholarGoogle ScholarCross RefCross Ref
  7. I. A. Ibragimov and K. E. Chernin, "On the unimodality of stable laws," Theory of Probability and its Apph'cations, vol. 4, pp. 417-419, 1959.Google ScholarGoogle ScholarCross RefCross Ref
  8. M. E. Johnson, "Computer generation of the exponential power distribution," Journal of Statistical Computation and Simulation, vol. 9, pp. 239- 240, 1979.Google ScholarGoogle ScholarCross RefCross Ref
  9. N. L. Johnson, "Systems of frequency curves generated by methods of translation," Biometrika, vol. 36, pp. 149-176, 1949.Google ScholarGoogle ScholarCross RefCross Ref
  10. N. L. Johnson, "Systems of frequency curves derived from the first law of Laplace," Tzabajos de Es- $adistica, vol. 5, pp. 283-291, 1954.Google ScholarGoogle Scholar
  11. N. L. Johnson and S. Kotz, "Encyclopedia of the Statistical Sciences," vols. 1-4 (1983), vols. 5-6 (1985), vol. 7 (1986), vols. 8-9 (1988), supplement (1989), John Wiley, New York,Google ScholarGoogle Scholar
  12. N. L. Johnson and S. Kotz, "Extended and multivariate Tukey lambda distributions," Biometrika, vol. 60, pp. 655-661, 1973.Google ScholarGoogle ScholarCross RefCross Ref
  13. M. Kanter, "Stable densities under change of scale and total variation inequalities," Annals of Probability, vol. 3, pp. 697-707, 1975.Google ScholarGoogle ScholarCross RefCross Ref
  14. T. Kawata, Fourier Analysis in Probability Theory, Academic Press, New York, N.Y., 1972.Google ScholarGoogle Scholar
  15. L. B. Klebanov, G. V. Maniya, and I. A. Melamed, "A problem of Zolotarev and analogs of infinitely divisible and stable distributions in a scheme for summing a random number of random variables," Theory of Probability and its Applications, vol. 29, pp. 791-794, 1984.Google ScholarGoogle ScholarCross RefCross Ref
  16. R. ~. Laha, "On a class of unimodal distributions," Proceedings of the American Mathematical Society, vol. 12, pp. 181-184, 1961.Google ScholarGoogle ScholarCross RefCross Ref
  17. R. G. Laha and E. Lukacs, "On a problem connected with quadratic regression," Biometrika, vol. 47, pp. 335-343, 1960.Google ScholarGoogle ScholarCross RefCross Ref
  18. Yu. V. Linnik, "Linear forms and statistical criteria: I, II," Selected Translations in Mathematical Statistics and Probability, vol. 3, pp. 1-40, 41- 90, 1962.Google ScholarGoogle Scholar
  19. E. Lukacs, Characteristic Functions, Griffin, London, 1970.Google ScholarGoogle Scholar
  20. R. N. Pillai, "Semi-c~ Laplace distributions," Corn~ munications in Statistics ~ Theory and Methods, vol. 14, pp. 991-1000, 1985.Google ScholarGoogle ScholarCross RefCross Ref
  21. i. Popescu, "Algorithms for generating the logistic variable," Economic Computation and E~onomic Cybernetics Studies and Research, vol. 10(1), pp. 55- 61, 1976.Google ScholarGoogle Scholar
  22. J. S. Ramberg and B. W. Schmeiser, "An approximate method for generating asymmetric random variables," Communications of the A CM, vol. 17, pp. 78-82, 1974. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. B. W. Schmeiser and S. J. Deutch, "A versatile four parameter family of probability distributions suitable for simulation," AIEE Transactions, vol. 9, pp. 176-182, 1977.Google ScholarGoogle ScholarCross RefCross Ref
  24. P. R. Tadikamalla, "A look at the Burr and related distributions," international Statistical Review, vol. 48, pp. 337-344, 1980.Google ScholarGoogle Scholar
  25. P. R. Tadikamalla, "Random sampling from the exponential power distribution," Journal of the American Statistical Association, vol. 75, pp. 683-686, 1980.Google ScholarGoogle ScholarCross RefCross Ref
  26. P. R. Tadikamalla, "On simulating non-normal distributions," Psychometrika, vol. 45, pp. 273-279, 1980.Google ScholarGoogle ScholarCross RefCross Ref
  27. P. R. Tadikamalla and N. L. Johnson, "Tables to facilitate fitting Tadikamalla and Johnson's LB distributions," Communications in Statistics, Series Simula6on, vol. 19, pp. 1201-1229, 1990.Google ScholarGoogle ScholarCross RefCross Ref
  28. J. W. Tukey, "The practical relationship between the common transformations of percentages of counts and of amounts," Technical Report 36, Statistical Techniques Research Group, Princeton University, 1960.Google ScholarGoogle Scholar
  29. G. Ulrich, "Computer generation of distributions on the m-sphere," Applied Statistics, vol. 33, pp. 158- 163, 1984.Google ScholarGoogle ScholarCross RefCross Ref
  30. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, 1927 (1980).Google ScholarGoogle Scholar
  31. V. M. Zolotarev, "On the representation of stable laws by integrals," Selected Translations in Mathematical Statistics and Probability, vol. 6, pp. 84- 88, 1966.Google ScholarGoogle Scholar
  32. V. M. Zolotarev, One-Dimensional Stable Distributions, American Mathematical Society, Providence, R.I., 1986.Google ScholarGoogle Scholar

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  • Published in

    cover image ACM Conferences
    WSC '96: Proceedings of the 28th conference on Winter simulation
    November 1996
    1527 pages
    ISBN:0780333837

    Publisher

    IEEE Computer Society

    United States

    Publication History

    • Published: 8 November 1996

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    WSC '96 Paper Acceptance Rate128of187submissions,68%Overall Acceptance Rate3,413of5,075submissions,67%

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