[R] Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

[hadley wickham]

On Tue, Sep 23, 2008 at 9:59 AM, zhijie zhang <epistat at gmail.com> wrote:
> Dear R users,
>  I hope to explain the concepts of skewness and kurtosis by generating
> series of distributions with same skewness and different kurtosis or  with
> same kurtosis and different skewness, but it seems that i cannot find the
> right functions.
>  I have searched the mailing list, but no answers were found.
>  Is it possible to do that in R? Which function could be used?
>  Thanks a lot.

You might want to have a look at Pearson's type IV distribution.  This
document, http://www-cdf.fnal.gov/publications/cdf6820_pearson4.pdf,
provides a pretty good introduction, and I think you can use the
method of moments in reverse to fix the first four moments (~mean, sd,
skewness, kurtosis) and then derive the appropriate parameters of the
Pearson's distribution.

Hadley


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