[R] Fitting Mixture of Non-Central Student's t Distributions

[Ingmar Visser]

Dear Susanne & Dave,

The gamlss package family has an enormous variety of distributions and  
a function to combine
them into mixtures. In particular, the 3 parameter student's t and the  
4 parameter generalized t
distribution.

Hth, Ingmar

On 15 Jun 2009, at 17:12, David Hunter wrote:

> Hi Susanne.  The mixtools package does not do this automatically and  
> I would be surprised if there were any package that does.  However,  
> it's not in principle too difficult to write code to implement an EM  
> algorithm to search for a maximum likelihood estimator in a finite  
> mixture model.   Check out a reference on finite mixture models that  
> discusses EM algorithms (e.g., Section 2.2 of http://www.stat.psu.edu/~dhunter/papers/mixtools.pdf 
>  although there are undoubtedly better references out there for this  
> purpose).
>
> In the case of components that are assumed to be noncentral Student  
> t distributions, you may have a bit of trouble since if I remember  
> correctly, it is not easy to do MLE even for the non-mixture case  
> here.  That said, in general, writing an EM algorithm for the finite- 
> mixture-model case is not much more difficult computationally than  
> writing code for MLE in the non-mixture case.  This means that you  
> could try expanding your search to include other packages that might  
> do MLE for the (non-mixture) case of noncentral t distributions.  If  
> such a package exists, then it shouldn't be too hard to write your  
> own mixture-model EM wrapper.
>
> Hope this helps.  Good luck!
> Dave
>
>
>
> David Hunter
> Associate professor
> Department of Statistics
> Penn State University
> Phone:  (814) 863-0979
> Fax:  (814) 863-7114
> www.stat.psu.edu/~dhunter
>
>
>
> On Jun 13, 2009, at 7:54 AM, Balzer Susanne wrote:
>
>> Dear all,
>>
>> I am attempting to model some one-dimensional data using a mixture  
>> model
>> of non-central Student's t distributions. However, I haven't been  
>> able
>> to find any R package that provides this functionality.
>> Could there be a way to "manipulate" the EM algorithms from the  
>> mixdist
>> or mixtools package to fit the model, or do you have any other
>> suggestions?
>>
>> If anyone could help me out, I would be extremely grateful.
>>
>> Kind regards,
>>
>> Susanne Balzer
>>
>>
>>
>> ****************************
>> Susanne Balzer
>> PhD Student
>> Institute of Marine Research
>> N-5073 Bergen, Norway
>> Phone: +47 55 23 69 45
>> susanne.balzer at imr.no
>> www.imr.no
>>
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>
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