From: Chaouch, Aziz <achaouch_at_nrcan.gc.ca>

Date: Sat 27 May 2006 - 04:50:59 EST

Date: Sat 27 May 2006 - 04:50:59 EST

Thanks Ravi! That's probably more than what I need. I suppose I'll have
to get back to you for some more explanations but for now I'm trying to
apply the log-likelihood (likelihood) that you defined to the fitdistr
function or use the log-likelihood with optim().

Thanks again, that's really helpful!

Regards,

Aziz

-----Original Message-----

From: Ravi Varadhan [mailto:rvaradhan@jhmi.edu]
Sent: May 26, 2006 12:18 PM

To: Chaouch, Aziz

Cc: r-help@stat.math.ethz.ch

Subject: RE: [R] Maximum likelihood estimate of
bivariatevonmises-weibulldistribution

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: rvaradhan@jhmi.edu Webpage:http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html ------------------------------------------------------------------------ --Received on Sat May 27 05:08:20 2006

> -----Original Message-----

> From: r-help-bounces@stat.math.ethz.ch [mailto:r-help-

> bounces@stat.math.ethz.ch] 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:Dimitris.Rizopoulos@med.kuleuven.be]> 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" <achaouch@NRCan.gc.ca>:>> > 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:dimitris.rizopoulos@med.kuleuven.be]> > Sent: May 12, 2006 9:57 AM> > To: Chaouch, Aziz; hydinghua@gmail.com> > 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" <achaouch@NRCan.gc.ca>> > To: "Dimitris Rizopoulos" <dimitris.rizopoulos@med.kuleuven.be>;> > <hydinghua@gmail.com>> > 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:dimitris.rizopoulos@med.kuleuven.be]> > 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" <hydinghua@gmail.com>> > To: "Chaouch, Aziz" <achaouch@nrcan.gc.ca>> > 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 <achaouch@nrcan.gc.ca> 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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