Hi Aziz, I am attaching a file that contains the functions that I wrote to compute the MLE for a binary vonMises mixture, using the EM algorithm. It also contains a simulation example. Let me know if you have any trouble.
Hope this is helpful, Ravi. -------------------------------------------------------------------------- Ravi Varadhan, Ph.D. Assistant Professor, The Center on Aging and Health Division of Geriatric Medicine and Gerontology Johns Hopkins University Ph: (410) 502-2619 Fax: (410) 614-9625 Email: [EMAIL PROTECTED] Webpage:http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html -------------------------------------------------------------------------- > -----Original Message----- > From: [EMAIL PROTECTED] [mailto:r-help- > [EMAIL PROTECTED] On Behalf Of Chaouch, Aziz > Sent: Friday, May 26, 2006 12:02 PM > To: Dimitrios Rizopoulos > Cc: r-help@stat.math.ethz.ch > Subject: Re: [R] Maximum likelihood estimate of bivariatevonmises- > weibulldistribution > > Hi, > > I'm still strugling with this copula model but this seems to be the way > to go. I'm now trying to model the marginal distributions and and for > wind direction I use a mixture of 2 von mises. I'd like to estimate all > the parameters (m1,m1,kappa1,kappa2,p) by maximizing the likelihood but > I don't know how to define the likelihood (or log-likelihood) of a > mixture of 2 Von Mises to use it with the function fitDistr in the MASS > package. Can you help me define this likelihood function and use it > through the fitDistr function? > > Thanks, > > Aziz > > -----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
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