R help - May 2006 - Maximum likelihood estimate of bivariate vonmises-weibull distribution

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. 

First is this a stupid question? I'm a newbie in statistics and R :)

Is it possible to do it in R?

Is there a way to estimate the parameters of the bivariate distribution
using maximum likelihood? Do you have some hints on how to do this in R
(with optim for example)?

The second problem is that the distribution of wind direction is
sometime bimodal (likely to be due to topography). Is it possible to
model the distribution as a mixture of 2 von mises distribution and
build a awfully complex joint distribution that would be "mixture of 2
von mises - weibull"????

Thanks a lot,

Aziz



	[[alternative HTML version deleted]]

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.

First is this a stupid question? I'm a newbie in statistics and R
:)
>
> Is it possible to do it in R?
>
> Is there a way to estimate the parameters of the bivariate distribution
> using maximum likelihood? Do you have some hints on how to do this in R
> (with optim for example)?
>
> The second problem is that the distribution of wind direction is
> sometime bimodal (likely to be due to topography). Is it possible to
> model the distribution as a mixture of 2 von mises distribution and
> build a awfully complex joint distribution that would be "mixture of 2
> von mises - weibull"????

Yes, you can model wind direction as a mixture of two von miese
distributions, but be aware of the computation burden. In R, optim() is a
good condidate function for maximization if the number of parameters are not
large.

Thanks a lot,
>
> Aziz
>
>
>
>         [[alternative HTML version deleted]]
>
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>
	[[alternative HTML version deleted]]

----- 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


> First is this a stupid question? I'm a newbie in statistics and R :)
>>
>> Is it possible to do it in R?
>>
>> Is there a way to estimate the parameters of the bivariate 
>> distribution
>> using maximum likelihood? Do you have some hints on how to do this 
>> in R
>> (with optim for example)?
>>
>> The second problem is that the distribution of wind direction is
>> sometime bimodal (likely to be due to topography). Is it possible 
>> to
>> model the distribution as a mixture of 2 von mises distribution and
>> build a awfully complex joint distribution that would be "mixture 
>> of 2
>> von mises - weibull"????
>
>
> Yes, you can model wind direction as a mixture of two von miese
> distributions, but be aware of the computation burden. In R, optim() 
> is a
> good condidate function for maximization if the number of parameters 
> are not
> large.
>
> Thanks a lot,
>>
>> Aziz
>>
>>
>>
----
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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