[R] Maximum likelihood estimate of bivariate vonmises-weibulldistribution

[Chaouch, Aziz]

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 at 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 at 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 at med.kuleuven.be] 
> Sent: May 12, 2006 9:57 AM
> To: Chaouch, Aziz; hydinghua at gmail.com
> Cc: r-help at 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 at NRCan.gc.ca>
> To: "Dimitris Rizopoulos" <dimitris.rizopoulos at med.kuleuven.be>;
> <hydinghua at gmail.com>
> Cc: <r-help at 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 at med.kuleuven.be]
> Sent: May 12, 2006 3:01 AM
> To: Philip He; Chaouch, Aziz
> Cc: r-help at stat.math.ethz.ch
> Subject: Re: [R] Maximum likelihood estimate of bivariate
> vonmises-weibulldistribution
> 
> 
> ----- Original Message -----
> From: "Philip He" <hydinghua at gmail.com>
> To: "Chaouch, Aziz" <achaouch at nrcan.gc.ca>
> Cc: <r-help at 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 at 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
> 
> 
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> 
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