[R] Maximum likelihood estimate of bivariatevonmises-weibulldistribution
Ravi Varadhan
rvaradhan at jhmi.edu
Fri May 26 18:18:07 CEST 2006
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 at jhmi.edu
Webpage:http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
--------------------------------------------------------------------------
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-
> bounces at stat.math.ethz.ch] On Behalf Of Chaouch, Aziz
> Sent: Friday, May 26, 2006 12:02 PM
> To: Dimitrios Rizopoulos
> Cc: r-help at 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 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
> >
> >
> > Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
> >
> >
> > Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
> >
> >
>
>
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