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

Patrick Burns patrick at burns-stat.com
Tue Aug 26 19:47:45 CEST 2008

I suspect that the 'sn' package (as in skew-normal)
is the natural target of the search.

Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
(home of S Poetry and "A Guide for the Unwilling S User")

John Frain wrote:
> 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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