R help - Sep 2008 - Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

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.

-- 
With Kind Regards,

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[***********************************************************************]
Zhi Jie,Zhang ,PHD
Tel:+86-21-54237149
Dept. of Epidemiology,School of Public Health,Fudan University
Address:No. 138 Yi Xue Yuan Road,Shanghai,China
Postcode:200032
Email:epistat@gmail.com <Email%3Aepistat@gmail.com>
Website: www.statABC.com
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Hi,

Certainly it's possible. Use any distribution function as long as you
can change its skewness and kurtosis, e.g. the Chi-square
distribution. The corresponding R functions are p*, q*, d*, and r* - I
think you know these functions already (e.g. rchisq()).

The only thing that you should be clear about is the relationship
between the arguments of distribution functions in R and those in a
certain theoretical distribution. Refer to
http://en.wikipedia.org/wiki/Probability_distribution if you don't
remember those formulae for skewness and kurtosis.

Regards,
Yihui
--
Yihui Xie <xieyihui at gmail.com>
Phone: +86-(0)10-82509086 Fax: +86-(0)10-82509086
Mobile: +86-15810805877
Homepage: http://www.yihui.name
School of Statistics, Room 1037, Mingde Main Building,
Renmin University of China, Beijing, 100872, China



On Tue, Sep 23, 2008 at 10:59 PM, 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.
>
> --
> With Kind Regards,
>
> oooO:::::::::
> (..):::::::::
> :\.(:::Oooo::
> ::\_)::(..)::
> :::::::)./:::
> ::::::(_/::::
> :::::::::::::
> [***********************************************************************]
> Zhi Jie,Zhang ,PHD
> Tel:+86-21-54237149
> Dept. of Epidemiology,School of Public Health,Fudan University
> Address:No. 138 Yi Xue Yuan Road,Shanghai,China
> Postcode:200032
> Email:epistat at gmail.com <Email%3Aepistat at gmail.com>
> Website: www.statABC.com
> [***********************************************************************]
> oooO:::::::::
> (..):::::::::
> :\.(:::Oooo::
> ::\_)::(..)::
> :::::::)./:::
> ::::::(_/::::
> :::::::::::::
>

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


-- 
http://had.co.nz/

Check out JohnsonFit in SuppDists.

On Tue, Sep 23, 2008 at 10:59 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.
>
> --
> With Kind Regards,
>
> oooO:::::::::
> (..):::::::::
> :\.(:::Oooo::
> ::\_)::(..)::
> :::::::)./:::
> ::::::(_/::::
> :::::::::::::
> [***********************************************************************]
> Zhi Jie,Zhang ,PHD
> Tel:+86-21-54237149
> Dept. of Epidemiology,School of Public Health,Fudan University
> Address:No. 138 Yi Xue Yuan Road,Shanghai,China
> Postcode:200032
> Email:epistat at gmail.com <Email%3Aepistat at gmail.com>
> Website: www.statABC.com
> [***********************************************************************]
> oooO:::::::::
> (..):::::::::
> :\.(:::Oooo::
> ::\_)::(..)::
> :::::::)./:::
> ::::::(_/::::
> :::::::::::::
>
>        [[alternative HTML version deleted]]
>
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