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 <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:: ::\_)::(..):: :::::::)./::: ::::::(_/:::: :::::::::::::