Aziz, I think you can take a look at http://gro.creditlyonnais.fr/content/rd/home_copulas.htm There is a lot of really good introductions to copulae, in pdf in english and in french also.
Etienne At 10:06 15/05/2006 -0400, Chaouch, Aziz wrote: > Hi Dimitrios, > >1) you propose to compare copula models using the same Kendall's tau. If >I understand correctly, I should use the Kendall's tau between wind >direction and wind speed and then compute the different copula models >using that Kendall's tau, right? However as Wind direction is a circular >variable modelled with a Von Mises distribution (or a mixture of), >Kendall's tau should be inefficient at measuring a circular-linear rank >correlation. I'm aware that Mardia (1976) has proposed a circular-linear >correlation coefficient (based on Pearson's one) but I'm not sure about >the existence of a circular-linear version of Kendall's tau. > >2) Anyway I'm probably better using the fitMvdc function in package >copula to estimate the copula model parameter by MLE (doing this for >every copula model and see which one better fits my data). However do >you have recommandations on how to choose good starting values for the >parameter in the fitMvdc function? In the help of the fitMvdc function >(see below), the starting values for a gumbel copula are c(1,1,2) >although the gumbel copula has only one parameter (not three). So what >does this vector c(1,1,2) means? > >gmb <- gumbelCopula(3, dim=2) >myMvd <- mvdc(gmb, c("exp","exp"), list(list(rate=2),list(rate=4))) >x <- rmvdc(myMvd, 1000) >fit <- fitMvdc(x, myMvd, c(1,1,2)) > >3) How did you do to choose the copula parameter that is associated to a >specific Kendall's tau in your example? Would such a parameter (based on >a measured Kendall's tau on my variables providing that such a measure >for circular-linear relationships exists) be a good starting value as a >parameter for each copula model?? > >Thanks a lot! > >Aziz > > >PS: the email address of the maintainer of copula package seems to be >not working > >-----Original Message----- >From: Dimitrios Rizopoulos [mailto:[EMAIL PROTECTED] >Sent: May 12, 2006 4:35 PM >To: Chaouch, Aziz >Subject: RE: [R] Maximum likelihood estimate of bivariate >vonmises-weibulldistribution > >look at the following code: > >library(copula) >par(mfrow = c(2, 2)) >x <- mvdc(normalCopula(sin(0.5 * pi /2)), c("norm", "norm"), >list(list(mean = 0, sd = 1), list(mean = 0, sd = 1))) contour(x, dmvdc, >xlim = c(-2.7, 2.7), ylim = c(-2.7, 2.7)) > >x <- mvdc(frankCopula(5.736276), c("norm", "norm"), list(list(mean = 0, >sd = 1), list(mean = 0, sd = 1))) contour(x, dmvdc, xlim = c(-2.7, 2.7), >ylim = c(-2.7, 2.7)) > >x <- mvdc(gumbelCopula(2), c("norm", "norm"), list(list(mean = 0, sd = >1), list(mean = 0, sd = 1))) contour(x, dmvdc, xlim = c(-2.7, 2.7), ylim >= c(-2.7, 2.7)) > >x <- mvdc(claytonCopula(2), c("norm", "norm"), list(list(mean = 0, sd = >1), list(mean = 0, sd = 1))) contour(x, dmvdc, xlim = c(-2.7, 2.7), ylim >= c(-2.7, 2.7)) > > >the values of the association parameter I've chosen in each copula >correspond to Kendall's tau 0.5; assuming also standard normal >marginal distributions look at the different shapes you get! > >If possible try something similar for you case (i.e., using von Mises >and Weibull marginals) and check if the association shape for a >specific copula is more appropriate for your application. If this is >not possible fit models assumig different copulas and check which one >provides a better fit to your data. > >I hope it helps. > >Best, >Dimitris > > > >Quoting "Chaouch, Aziz" <[EMAIL PROTECTED]>: > >> Hi Dimitris, >> >> I'm not sure to understand your suggestion. How would you build that >> contour plot for a particular copula and on what is computed the >> Kendall's tau? >> >> Thanks, >> >> Aziz >> >> -----Original Message----- >> From: Dimitris Rizopoulos >> [mailto:[EMAIL PROTECTED] >> Sent: May 12, 2006 9:57 AM >> To: Chaouch, Aziz; [EMAIL PROTECTED] >> Cc: r-help@stat.math.ethz.ch >> Subject: Re: [R] Maximum likelihood estimate of bivariate >> vonmises-weibulldistribution >> >> the choice of the copula is, in fact, a model selection problem. >> First, you could have a look at the contour plots of different >> copulas >> (preferably for the same value of Kendall's tau), and decide if some >> of >> them assume a more appropriate association structure for your >> application, compared to the others. Afterwards, you may fit various >> copula functions, check the fit on the data, compute AIC (since >> these >> are typically not nested models), etc. >> >> regarding the Von Mises distribution and if could be used in mvdc(), >> that I don't know. It'd be better to contact the copula package >> maintainer and ask. >> >> I hope it helps. >> >> Best, >> Dimitirs >> >> ---- >> Dimitris Rizopoulos >> Ph.D. Student >> Biostatistical Centre >> School of Public Health >> Catholic University of Leuven >> >> Address: Kapucijnenvoer 35, Leuven, Belgium >> Tel: +32/(0)16/336899 >> Fax: +32/(0)16/337015 >> Web: http://www.med.kuleuven.be/biostat/ >> http://www.student.kuleuven.be/~m0390867/dimitris.htm >> >> >> ----- Original Message ----- >> From: "Chaouch, Aziz" <[EMAIL PROTECTED]> >> To: "Dimitris Rizopoulos" <[EMAIL PROTECTED]>; >> <[EMAIL PROTECTED]> >> Cc: <r-help@stat.math.ethz.ch> >> Sent: Friday, May 12, 2006 3:13 PM >> Subject: RE: [R] Maximum likelihood estimate of bivariate >> vonmises-weibulldistribution >> >> >> Thanks a lot! I wasn't aware of that copula package and it could well >> be >> appropriate to use it for my application. However if I read the >> copula >> help correctly, I still need to know what kind of copula to use to >> link >> the distribution of wind speeds and directions. Is there a way to >> determine this in R? >> >> Moreover can I use the Von Mises distribution from the circular or >> CircStats package into the mvdc function of the copula package or >> does >> the mvdc function only recognize distributions available "natively" >> within R? >> >> Thanks again to all, your help is highly appreciated for a newbie >> like >> me! >> >> Regards, >> >> Aziz >> >> -----Original Message----- >> From: Dimitris Rizopoulos >> [mailto:[EMAIL PROTECTED] >> Sent: May 12, 2006 3:01 AM >> To: Philip He; Chaouch, Aziz >> Cc: r-help@stat.math.ethz.ch >> Subject: Re: [R] Maximum likelihood estimate of bivariate >> vonmises-weibulldistribution >> >> >> ----- Original Message ----- >> From: "Philip He" <[EMAIL PROTECTED]> >> To: "Chaouch, Aziz" <[EMAIL PROTECTED]> >> Cc: <r-help@stat.math.ethz.ch> >> Sent: Thursday, May 11, 2006 11:21 PM >> Subject: Re: [R] Maximum likelihood estimate of bivariate >> vonmises-weibulldistribution >> >> >> > On 5/11/06, Chaouch, Aziz <[EMAIL PROTECTED]> wrote: >> >> >> >> Hi, >> >> >> >> I'm dealing with wind data and I'd like to model their >> distribution >> >> in order to simulate data to fill-in missing values. Wind >> direction >> >> are typically following a vonmises distribution and wind speeds >> >> follow a weibull distribution. I'd like to build a joint >> distribution >> >> >> of directions and speeds as a VonMises-Weibull bivariate >> >> distribution. >> > >> > >> > In order to built a bivariate distribution from two marginal >> > distributions (wind direction, wind speed) , more information is >> > needed to specify the relation between these two marginal >> > distributions.For example, a conditional distribution may help. >> > >> >> >> An alternative in such cases (i.e., when marginals are available but >> the >> joint is difficult to postulate) is to use copulas, which can >> construct >> multivariate distributions from univariate marginals. If this is >> appropriate for this application, the "copula" package might be of >> help. >> >> Best, >> Dimitris >> >> --- >> Dimitris Rizopoulos >> Ph.D. Student >> Biostatistical Centre >> School of Public Health >> Catholic University of Leuven >> >> Address: Kapucijnenvoer 35, Leuven, Belgium >> Tel: +32/(0)16/336899 >> Fax: +32/(0)16/337015 >> Web: http://www.med.kuleuven.be/biostat/ >> http://www.student.kuleuven.be/~m0390867/dimitris.htm >> >> >> Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm >> >> >> Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm >> >> > > >Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm > >______________________________________________ >R-help@stat.math.ethz.ch mailing list >https://stat.ethz.ch/mailman/listinfo/r-help >PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html ====================================== + + Cuvelier Etienne + Assistant + FUNDP - Institut d'Informatique + rue Grandgagnage, 21 B-5000 Namur (Belgique) + tel: 32.81.72.49.93 fax: 32.81.72.49.67 + ====================================== Le plus simple écolier sait maintenant des vérités pour lesquelles Archimède eût sacrifié sa vie. [ Ernest Renan ] ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html