# [R] Maximum likelihood estimate of bivariate vonmises-weibulldistribution

Dimitris Rizopoulos dimitris.rizopoulos at med.kuleuven.be
Fri May 12 09:01:03 CEST 2006

```----- 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