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I am curious to learn whether there are any best practises in creating random variables for a Monte Carlo simulation using input such as skewness and kurtosis information of a particular distribution. Of course those need to be used in addition to the average and standard deviation.

My objective is to create a number series that better captures the shape of a distribution than just using the average and standard deviation.

A next question would be: what functions in Excel and/or R to use generate the numbers on this basis?

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  • $\begingroup$ One imagines that some of the comments from this question might lead in the right direction: stats.stackexchange.com/questions/2377/… $\endgroup$
    – russellpierce
    Jan 27, 2013 at 9:48
  • $\begingroup$ Per the help-file for the e1071 package in R on skewness and kurtosis there are several ways to calculate these quantities... do you have a preferred method for use in the answer you receive? D. N. Joanes and C. A. Gill (1998), Comparing measures of sample skewness and kurtosis. The Statistician, 47, 183–189. $\endgroup$
    – russellpierce
    Jan 27, 2013 at 9:54
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    $\begingroup$ Thanks @drknexus. Will have a look into it. Just doing a little more research myself and this article also might lead in the right direction: stackoverflow.com/questions/4807398/… $\endgroup$
    – Jochem
    Jan 27, 2013 at 11:08
  • $\begingroup$ Here another interesting discussion: stackoverflow.com/questions/1422247/… . I may have to experiment a bit with those approaches and then see whether one of them will lead to a good enough solution. $\endgroup$
    – Jochem
    Jan 27, 2013 at 11:29
  • $\begingroup$ Moments don't pin down distributions very well. You could perhaps consider using the Pearson distributions or the Johnson distributions, but they don't necessarily correspond to the original distributions you'd like to get. $\endgroup$
    – Glen_b
    Jan 28, 2013 at 7:57

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These features can be included in simulations from a symmetric distribution using transformations that control skewness and kurtosis such as the Johnson-SU transformation, the g-and-h, the g-and-k, the sinh-arcsinh, and the LambertW tranformations (Tukey-type transformations). A quick google search gives you relevant references for these transformations. See also Transformation to increase kurtosis and skewness of normal r.v

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