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?
Best Answer
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