Abstract
A method of introducing a controlled degree of skew and kurtosis for Monte Carlo studies was derived. The form of such a transformation on normal deviates [X ≈N(0, 1)] isY =a +bX +cX 2 +dX 3. Analytic and empirical validation of the method is demonstrated.
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Brown, B. R., & Lathrop, R. L.The effects of violations of assumptions upon certain tests of the product moment correlation coefficient. Paper presented to American Educational Research Association Annual Meeting, February 5, 1971.
References
Andrews, D. F., Bickel, P. J., Hampel, F. R., Huber, P. J., Rogers, W. H., & Tukey, J. W.Robust estimation of location: Survey and advances. Princeton: Princeton University Press, 1972.
Brewer, J. K., & Hills, J. R. Skew and Correction for Explicit Univariate Selection. Proceedings of the 76th Annual Convention of the American Psychological Association, 1968, 218–220.
Brewer, J. K., & Hills, J. R. Univariate selection: The effect of correlation, degree of skew, and degree of restriction.Psychometrika, 1969,34, 347–361.
Brown, K. M., & Conte, S. D. The solution of simultaneous non-linear equations.Proceedings of the 22nd National Conference, Association for Computing Machinery. Washington D.C.: Thompson Book Co., 1967, 111–114.
Chambers, J. M., Mallows, C. L., & Stuck, B. W. A method for simulating stable random variables.Journal of the American Statistical Association, 1976,354, 340–344.
Church, A. E. R. On the means and squared standard deviations of small samples from any population.Biometrika, 1926,18, 321–394.
Devlin, S. J., Gnadadesikan, R., & Kettenring, J. R. Robust estimation and outlier detection with correlation coefficients.Biometrika, 1975,62, 531–545.
Donaldson, T. S. Robustness of theF-test to errors of both kinds and the correlation between the numerator and denominator of theF ratio.Journal of the American Statistical Association, 1963,332, 660–676.
Evans, W. D. On the variance of estimates of the standard deviation and variance.Journal of the American Statistical Association, 1951,46, 220–224.
International Mathematical and Statistical Libraries: Computer Subroutine Libraries in Mathematics and Statistics (Vol. I). Houston, Texas: Suite 510, 6200 Hillcroft, 1974.
Gulliksen, H.Theory of mental tests. New York: Wiley, 1950.
Hammersley, J. M., & Handscomb, D. C.Monte carlo methods. London: Metheun & Co. Ltd., 1965.
Kendall, M. C., & Stewart, A.The advanced theory of statistics, (Vol. 1). London: Charles Griffin & Co., Ltd., 1969.
Knuth, D. E.The art of computer programming: Semi-numerical algorithms, (Vol. 2). Reading, Mass.: Addison-Wesley Pub. Co. 1969.
Patnaik, P. B. The non-central chi square andF distributions and their applications.Biometrika, 1949,36, 202–232.
Pearson, E. S., & Please, N. W. Relation between the shape of population distribution of four simple test statistics.Biometrika, 1975,62, 223–241.
Ramberg, J. R. & Schmeiser, B. W. An approximate method for generating asymmetric random variables.Communications of the Association for Computing Machinery, 1974,17, 78–82.
Scheffé, H.The analysis of variance. New York: John Wiley & Sons. 1959.
“Sophister”. Discussion of small samples drawn from an infinite skew population.Biometrika, 1928,20A, 389–423.
Tukey, J. W. A survey of sampling from contaminated distributions. In I. Olkin [Ed.]Contributions to probability and statistics. Stanford, Cal.: Stanford University Press, 1960, 448–485.
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This work was done while the author was at the University of Illinois at Champaign-Urbana.
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Fleishman, A.I. A method for simulating non-normal distributions. Psychometrika 43, 521–532 (1978). https://doi.org/10.1007/BF02293811
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DOI: https://doi.org/10.1007/BF02293811