[R] MLE for a t distribution

[Barbara Gonzalez]

Thank you.

I actually found fitdistr() in the package MASS, that "estimates" the
df, but it does a very bad job. I know that the main problem is that
the t distribution has a lot of local maxima, and of course, when
k->infty we have the Normal distribution, which has nice and easy to
obtain MLEs.

I will try re-parametrizing k, but I doubt this will solve the problem
with the multiple local maxima.

I would like to implement something like the EM algorithm to go around
this problem, but I don't know how to do that.

Barbara

On Thu, Dec 10, 2009 at 2:59 PM, Albyn Jones <jones at reed.edu> wrote:
> k -> infinity gives the normal distribution.  You probably don't care
> much about the difference between k=1000 and k=100000, so you might
> try reparametrizing df on [1,infinity) to a parameter on [0,1]...
>
> albyn
>
> On Thu, Dec 10, 2009 at 02:14:26PM -0600, Barbara Gonzalez wrote:
>> Given X1,...,Xn ~ t_k(mu,sigma) student t distribution with k degrees
>> of freedom, mean mu and standard deviation sigma, I want to obtain the
>> MLEs of the three parameters (mu, sigma and k). When I try traditional
>> optimization techniques I don't find the MLEs. Usually I just get
>> k->infty. Does anybody know of any algorithms/functions in R that can
>> help me obtain the MLEs? I am especially interested in the MLE for k,
>> the degrees of freedom.
>>
>> Thank you!
>>
>> Barbara
>>
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>