A method for simulating non-normal distributions


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 [XN(0, 1)] isY =a +bX +cX 2 +dX 3. Analytic and empirical validation of the method is demonstrated.

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Correspondence to Allen I. Fleishman.

Additional information

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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Key words

  • computer simulation
  • departures from normality
  • kurtosis
  • Monte Carlo study
  • skew