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 <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> 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 <[EMAIL PROTECTED]> >> 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 <[EMAIL PROTECTED]> 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:[EMAIL PROTECTED] <[EMAIL PROTECTED]> >> > 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:[EMAIL PROTECTED] > Website: www.statABC.com > [***********************************************************************] > oooO::::::::: > (..)::::::::: > :\.(:::Oooo:: > ::\_)::(..):: > :::::::)./::: > ::::::(_/:::: > ::::::::::::: > ______________________________________________ R-help@r-project.org 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.
