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

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zhijie zhang

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,

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:[hidden email] <Email%[hidden email]>
Website: www.statABC.com
[***********************************************************************]
oooO:::::::::
(..):::::::::
:\.(:::Oooo::
::\_)::(..)::
:::::::)./:::
::::::(_/::::
:::::::::::::

[[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Yihui Xie

Re: Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

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 <[hidden email]>
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 <[hidden email]> 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:[hidden email] <Email%[hidden email]>
> Website: www.statABC.com
> [***********************************************************************]
> oooO:::::::::
> (..):::::::::
> :\.(:::Oooo::
> ::\_)::(..)::
> :::::::)./:::
> ::::::(_/::::
> :::::::::::::
>

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

hadley wickham

Re: Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

In reply to this post by zhijie zhang

On Tue, Sep 23, 2008 at 9:59 AM, zhijie zhang <[hidden email]> 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/

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

zhijie zhang

Re: Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

In reply to this post by Yihui Xie

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 <[hidden email]> 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 <[hidden email]>
> 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 <[hidden email]> 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:[hidden email] <Email%[hidden email]> <
> Email%[hidden email] <Email%[hidden email]>>
> > Website: www.statABC.com <http://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:[hidden email] <Email%[hidden email]>
Website: www.statABC.com
[***********************************************************************]
oooO:::::::::
(..):::::::::
:\.(:::Oooo::
::\_)::(..)::
:::::::)./:::
::::::(_/::::
:::::::::::::

[[alternative HTML version deleted]]

______________________________________________
[hidden email] mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Yihui Xie

Re: Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

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 <[hidden email]>
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 <[hidden email]> 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 <[hidden email]> 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 <[hidden email]>
>> 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 <[hidden email]> 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:[hidden email] <Email%[hidden email]>
>> > 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:[hidden email]
> Website: www.statABC.com
> [***********************************************************************]
> oooO:::::::::
> (..):::::::::
> :\.(:::Oooo::
> ::\_)::(..)::
> :::::::)./:::
> ::::::(_/::::
> :::::::::::::
>

Gabor Grothendieck

Re: Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

In reply to this post by zhijie zhang

Check out JohnsonFit in SuppDists.

On Tue, Sep 23, 2008 at 10:59 AM, zhijie zhang <[hidden email]> wrote:

Greg Snow-2

Re: Generating series of distributions with the same skewness and different kurtosis or with same kurtosis and different skewness?

And here is one way of using JohnsonFit to display how a distribution changes with changes in the moments:

library(TeachingDemos)
library(SuppDists)

tmpfun <- function(m1=0,m2=1,m3=-0.2,m4=3.7, xmin=-3, xmax=3){
parms <- JohnsonFit( c(m1,m2,m3,m4), 'use')
plot(function(x) dJohnson(x,parms), xmin, xmax)
}

tmplst <- list( Parameters=list(
m1=list('slider', init=0, from=-1, to=1, resolution=0.1),
m2=list('slider', init=1, from=0 , to=3, resolution=0.1),
m3=list('slider', init=-0.2, from=-1, to=1, resolution=0.1),
m4=list('slider', init=3.7, from=0 , to=10, resolution=0.5)),
xmin=list('numentry', init=-3, width=5),
xmax=list('numentry', init=3 , width=5) )

tkexamp( tmpfun, tmplst, plotloc='left' )

of course assuming that you have SuppDists and TeachingDemos packages installed, play around with this (and possibly change parameters and/or limits in tmplst) before demoing it as there are many combinations of the parameters that cause errors.

--
Gregory (Greg) L. Snow Ph.D.
Statistical Data Center
Intermountain Healthcare
[hidden email]
801.408.8111

> -----Original Message-----
> From: [hidden email] [mailto:r-help-bounces@r-
> project.org] On Behalf Of Gabor Grothendieck
> Sent: Wednesday, September 24, 2008 6:29 AM
> To: zhijie zhang
> Cc: [hidden email]
> Subject: Re: [R] Generating series of distributions with the same
> skewness and different kurtosis or with same kurtosis and different
> skewness?
>
> Check out JohnsonFit in SuppDists.
>
> On Tue, Sep 23, 2008 at 10:59 AM, zhijie zhang <[hidden email]>
> 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:[hidden email] <Email%[hidden email]>
> > Website: www.statABC.com
> >
> [**********************************************************************
> *]
> > oooO:::::::::
> > (..):::::::::
> > :\.(:::Oooo::
> > ::\_)::(..)::
> > :::::::)./:::
> > ::::::(_/::::
> > :::::::::::::
> >
> > [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > [hidden email] mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide http://www.R-project.org/posting-
> guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
>
> ______________________________________________
> [hidden email] mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-
> guide.html
> and provide commented, minimal, self-contained, reproducible code.