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

[Yihui Xie]

Well, let's take the Beta distribution for example. See
http://en.wikipedia.org/wiki/Beta_distribution for the formulae of
skewness and kurtosis. We can fix the skewness at, say, 2 and let
alpha = 1, then solve beta from the equation of "skewness = 2", you
will get beta =
1.8164966 or 0.1835034 approximately. Then you may compute the
kurtosis and find different beta values will lead to different
kurtosis values (-0.7315651 and 2.139547 respectively). Is this
example clear enough? Only need a little bit mathematical computation.

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 Wed, Sep 24, 2008 at 8:21 AM, zhijie zhang <epistat at gmail.com> wrote:
> Yihui,
>    Could you please show me an example?
>   What u have refered is clear for me, but i think the thing that i donot
> know how to handle with is to link the relationships between
> skewness/kurtosis and the distributions?
>   Thanks.
>
> On Tue, Sep 23, 2008 at 11:48 PM, Yihui Xie <xieyihui at gmail.com> wrote:
>>
>> 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::
>> > ::\_)::(..)::
>> > :::::::)./:::
>> > ::::::(_/::::
>> > :::::::::::::
>> >
>
>
>
> --
> 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
> Website: www.statABC.com
> [***********************************************************************]
> oooO:::::::::
> (..):::::::::
> :\.(:::Oooo::
> ::\_)::(..)::
> :::::::)./:::
> ::::::(_/::::
> :::::::::::::
>