Chaouch, Aziz
2006-May-12 20:47 UTC
[R] Maximum likelihood estimate of bivariate vonmises-weibulldistribution
Thanks Dimitris!!! That's much clearer now. Still have a lot of work to
do this weekend to understand every bit but your code will prove very
useful.
Cheers,
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
>
>
Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
Chaouch, Aziz
2006-May-15 14:06 UTC
[R] Maximum likelihood estimate of bivariate vonmises-weibulldistribution
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
Cuvelier Etienne
2006-May-15 14:24 UTC
[R] Maximum likelihood estimate of bivariate vonmises-weibulldistribution
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 > >______________________________________________ >R-help at 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=====================================+ + 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 + =====================================Le plus simple ?colier sait maintenant des v?rit?s pour lesquelles Archim?de e?t sacrifi? sa vie. [ Ernest Renan ]
Chaouch, Aziz
2006-May-26 16:02 UTC
[R] Maximum likelihood estimate of bivariate vonmises-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
>
>
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