[R-SIG-Finance] Generating Distributions with set skewness and kurtosis

John Frain frainj at tcd.ie
Tue Aug 26 18:37:39 CEST 2008

The normal distribution is symmetric and therefore can not be skewed.
The common measure of skewness when applied to the normal is 0.  The
kurtosis of the normal distribution is also fixed at 3.  If you want
to simulate a distribution with skew and heavy tails there are many
ways to do so.  A lot depends on what you want to do with the skewed
distributions.  You may look at mixtures of normal distributions or at
distributions which naturally allow skew such as the alpha-stable
distribution.  This latter has infinite variance so be careful as this
may or may not be what you want.  If you want to independently fix
location, spread, skew and kurtosis you will need a probability
distribution with 4 parameters.

John Frain

2008/8/26  <Matthias.Koberstein at hsbctrinkaus.de>:
> Hello,
> I am reaching out to you for help since I am struggeling to find a function
> to generate distributions with a set statistical properties as kurtosis and
> skewdness.
> Lets say I want to generate random variables following a "normal"
> distribution, but with skewness 2 and kurtosis 5.
> How would I do that, the most efficient way? Are there any packages for
> that? I had a quick look but were only able to find packages which
> calculate statistical
> distribution properties after having the data.
> Thank you very much
> Matthias
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John C Frain
Trinity College Dublin
Dublin 2
mailto:frainj at tcd.ie
mailto:frainj at gmail.com

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