Abstract
Simulations and experiments frequently demand the generation of random numbers that have specific distributions. This article describes which distributions should be used for. the most common problems and gives algorithms to generate the numbers. It is also shown that a commonly used permutation algorithm (Nilsson, 1978) is deficient.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Afflerbach, L. (1985). The pseudo-random number generators in Commodore and Apple microcomputers.Statistische Hefte,26, 321–333.
Aldridge, J. W. (1987). Cautions regarding random number generation on the Apple II.Behavior Research Methods, Instruments, & Computers,19, 397–399.
Atkinson, A. C. (1980). Tests of pseudo-random numbers.Applied Statistics,29, 164–171.
Best, D. J. (1979). Some easily programmed pseudo-random normal generators.Australian Computer Journal,11, 60–62.
Bissell, A. F. (1986). Ordered random selection without replacement.Applied Statistics,35, 73–75.
Box, G. E. P., &Jenkins, G. M. (1976).Time series analysis: Fore-casting and control. San Francisco’. Holden-Day.
Box, G. E. P., &Muller, M. E. (1958). A note on the generation of random normal deviates.Annals of Mathematical Statistics,29, 610–611.
Bradley, D. R. (1988).DATASIM. Lewiston, ME: Desktop Press.
Bradley, D. R., Senko, M. W., &Stewart, F. A. (1990). Statistical simulation on microcomputers.Behavior Research Methods, Instruments, & Computers,22, 236–246.
Brophy, A. L. (1985). Approximation of the inverse normal distribution function.Behavior Research Methods, Instruments, & Computers,17, 415–417.
Dreger, R. M. (1989). A BASIC program for the Shell-Metzner sort algorithm.Educational & Psychological Measurement,49, 619–622.
Dudewicz, E. 3., &Ralley, T. G. (1981).The handbook of random number generation and testing with TESTRAND computer code. Columbus, OH: American Sciences Press.
Dwyer, T., &Critchfield, M. (1978).BASIC and the Personalcomputer. Reading, MA: Addison-Wesley.
Edgell, S. E. (1979). A statistical check of the DECsystem-10 FORTRAN pseudorandom number generator.Behavior Research Methods & Instrumentation,11, 529–530.
Ellis, J. K. (1985). Distribution counting as a method for sorting test scores.Behavior Research Methods, Instruments, & Computers,17, 419–420.
Fishman, G. S., &Moore, L. R., Ill (1986). An exhaustive analysis of multiplicative congruential random number generators with modulus 231 - 1.SIAM Journal on Scientific & Statistical Computing,7, 24–45.
Green, B. F. (1963).Digital computers in research: An introduction for behavioral and social scientists. New York: McGraw-Hill.
Gruenberger, F., &Jaffray, G. (1965).Problems for computer solution. New York: Wiley.
Hays, W. L. (1988).Statistics. New York: Holt, Rinehart and Winston.
Kennedy, W. J., &Gentle, J. E. (1980).Statistical computing. New York: Marcel Dekker.
Knuth, D. E. (1973).The art of computer programming: Vol. 3. Sorting and searching. Reading, MA: Addison-Wesley.
Knuth, D. E. (1981).The art of computer programming: Vol. 2. Semi-numerical algorithms. Reading, MA: Addison-Wesley.
Kraner, H. C, Mohanty, S. G., &Lyons, J. C. (1980). Critical values of the Kolmogorov-Smirnoy one-sample test.Psychological Bulletin,88, 498–501.
Lordahl, D. S. (1988). Repairing the Microsoft BASIC RND function.Behavior Research Methods, Instruments, & Computers,20, 221–223.
Luce, R. D. (1986).Response times. New York: Oxford University Press.
MacLaren, N. M. (1989). The generation of multiple independent sequences of pseudorandom numbers.Applied Statistics,38, 351–359.
McLeod, A. I. (1985). A remark on Algorithm AS183: An efficient and portable pseudo-random number generator.Applied Statistics,34, 198–200.
Malmi, R. A. (1986). Intuitive covariation estimation.Memory & Cognition,14, 501–508.
Marsaglia, G. (1962). Random variables and computers. In J. Kozesnik (Ed.),Information theory, statistical decision functions, random processes: Transactions of the Third Prague Conference (pp. 499–510). Prague: Czechoslovak Academy of Sciences.
Marsagua, G., &Bray, T. A. (1964). A convenient method for generating normal variables.SIAM Review,6, 260–264.
Modianos, D. T., Scott, R. C., &Cornwell, L. W. (1987). Testing intrinsic random-number generators.Byte,12, 175–178.
Moses, L. E., &Oakford, R. V. (1963).Tables of random permutations. Stanford, CA: Stanford University Press.
Nance, R. E., &Overstreet, C. L. (1972). A bibliography on random number generators.Computer Review,13, 495–508.
Nilsson, T. H. (1978). Randomization without replacement using replacement without losing your place.Behavior Research Methods & Instrumentation,10, 419.
Press, W. H., Flannery, B. P., Teukolsky, S. A., &Vetterling, W. T. (1986).Numerical recipes: The art of scientific computing. Cambridge, U.K.: Cambridge University Press.
Ripley, B. D. (1983). Computer generation of random variables: A tutorial.International Statistical Review,51, 301–319.
Ripley, B. D. (1987).Stochastic simulation. New York: Wiley.
Sahai, H. (1979). A supplement to Sowey’s bibliography on random number generation and related topics.Journal of Statistical Computation & Simulation,10, 31–52.
Sowey, E. R. (1972). A chronological and classified bibliography on random number generation and testing.International Statistical Review,40, 355–371.
Sowey, E. R. (1978). A second classified bibliography on random number generation and testing.International Statistical Review,46, 355–371.
Sowey, E. R. (1986). A third classified bibliography on random number generation and testing.Journal of the Royal Statistical Society,149A, 83–107.
Strube, M. J. (1983). Tests of randomness for pseudorandom number generators.Behavior Research Methods & Instrumentation,15, 536–537.
von Neumann, J. (1951). Various techniques in connection with random digits.NBS Applied Mathematics Series,12, 36–38.
Wichmann, B. A., &Hill, J. D. (1982). Algorithm AS183: An efficient and portable pseudo random number generator.Applied Statistics,31, 188–190.
Wichmann, B. A., &Hill, J. D. (1984). An efficient and portable pseudo random number generator: Correction.Applied Statistics,33, 123.
Zeisel, H. (1986). A remark on Algorithm AS183: An efficient and portable pseudo-random number generator.Applied Statistics,35, 89.
Zelen, M., &Severo, N. C. (1964). Probability functions. In M. Abramowitz & I. A. Stegun (Eds.),Handbook of mathematical functions (pp. 925–995). New York: Dover.
Author information
Authors and Affiliations
Additional information
The author wishes to thank G. d’Ydewalle, as well as the editor and three reviewers, for helpful comments on earlier drafts of the manuscript.
Rights and permissions
About this article
Cite this article
Brysbaert, M. Algorithms for randomness in the behavioral sciences: A tutorial. Behavior Research Methods, Instruments, & Computers 23, 45–60 (1991). https://doi.org/10.3758/BF03203334
Received:
Accepted:
Issue date:
DOI: https://doi.org/10.3758/BF03203334