[R] Maximum likelihood estimate of bivariate vonmises-weibulldistribution
Cuvelier Etienne
ecu at info.fundp.ac.be
Mon May 15 16:24:32 CEST 2006
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: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
>>
>>
>
>
>Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
>
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======================================
+
+ 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
+
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pour lesquelles Archimède eût sacrifié sa vie.
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