[R] MLE for noncentral t distribution

[Balzer Susanne]

Hi,

Actually I am facing a similar problem. I would like to fit both an ordinary (symmetric) and a non-central t distribution to my (one-dimensional) data (quite some values.. > 1 mio.).
For the symmetric one, fitdistr or funInfoFun (using fitdistr) from the qAnalyst package should do the job, and for the non-central one.. am I right to use

gamlss(x ~ 1, family=GT()) ?

Anyway, I am a little unsure how to handle the degrees of freedom. I have the feeling that it is not smart to not hold them fixed, but how can I actually determine them?

If anyone could help me, I'd be really grateful... gamlss has a great documentation, but it's a bit overwhelming.

Kind regards

Susanne

****************************
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

> [R] MLE for noncentral t distribution
> Spencer Graves spencer.graves at pdf.com
> Fri May 9 16:32:47 CEST 2008
> 
>     * Previous message: [R] MLE for noncentral t distribution
>     * Next message: [R] MLE for noncentral t distribution
>     * Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]
> 
> Hi, Martin and Kate:
> 
> KATE:  Do you really want the noncentral t?  It has mean zero but
> strange tails created by a denominator following a noncentral
> chi-square.  The answer Martin gave is for a scaled but otherwise
> standard t, which sounds like what you want, since you said the "sample
> mean = 0.23, s = 4.04, etc.  A noncentral t has an additional
> "noncenrality parameter".
> 
> Hope this helps.
> Spencer
> 
> Martin Maechler wrote:
> >>>>>> "k" == kate  <yhsu6 at uiuc.edu>
> >>>>>>     on Thu, 8 May 2008 10:45:04 -0500 writes:
> >>>>>>
> >
> >     k> In my data,  sample mean =-0.3 and the histogram looks like t
> distribution;
> >     k> therefore, I thought non-central t distribution may be a good
> fit. Anyway, I
> >     k> try t distribution to get MLE. I found some warnings as
> follows; besides, I
> >     k> got three parameter estimators: m=0.23, s=4.04, df=1.66. I
> want to simulate
> >     k> the data with sample size 236 and this parameter estimates. Is
> the command
> >     k> rt(236, df=1.66)? Where should I put m and s when I do
> simulation?
> >
> >  m  +  s * rt(n, df= df)
> >
> > [I still hope this isn't a student homework problem...]
> >
> > Martin Maechler, ETH Zurich
> >
> >     k> m           s          df
> >     k> 0.2340746   4.0447124   1.6614823
> >     k> (0.3430796) (0.4158891) (0.2638703)
> >     k> Warning messages:
> >     k> 1: In dt(x, df, log) : generates NaNs
> >     k> 2: In dt(x, df, log) : generates NaNs
> >     k> 3: In dt(x, df, log) :generates NaNs
> >     k> 4: In log(s) : generates NaNs
> >     k> 5: In dt(x, df, log) : generates NaNs
> >     k> 6: In dt(x, df, log) : generates NaNs
> >
> >     k> Thanks a lot,
> >
> >     k> Kate
> >
> >     k> ----- Original Message -----
> >     k> From: "Prof Brian Ripley" <ripley at stats.ox.ac.uk>
> >     k> To: "kate" <yhsu6 at uiuc.edu>
> >     k> Cc: <r-help at r-project.org>
> >     k> Sent: Thursday, May 08, 2008 10:02 AM
> >     k> Subject: Re: [R] MLE for noncentral t distribution
> >
> >
> >     >> On Thu, 8 May 2008, kate wrote:
> >     >>
> >     >>> I have a data with 236 observations. After plotting the
> histogram, I
> >     >>> found that it looks like non-central t distribution. I would
> like to get
> >     >>> MLE for mu and df.
> >     >>
> >     >> So you mean 'non-central'?  See ?dt.
> >     >>
> >     >>> I found an example to find MLE for gamma distribution from
> "fitting
> >     >>> distributions with R":
> >     >>>
> >     >>> library(stats4) ## loading package stats4
> >     >>> ll<-function(lambda,alfa) {n<-200
> >     >>> x<-x.gam
> >     >>> -n*alfa*log(lambda)+n*log(gamma(alfa))-(alfa-
> >     >>> 1)*sum(log(x))+lambda*sum(x)} ## -log-likelihood function
> >     >>> est<-mle(minuslog=ll, start=list(lambda=2,alfa=1))
> >     >>>
> >     >>> Is anyone how how to write down -log-likelihood function for
> noncentral t
> >     >>> distribution?
> >     >>
> >     >> Just use dt. E.g.
> >     >>
> >     >>> library(MASS)
> >     >>> ?fitdistr
> >     >>
> >     >> shows you a worked example for location, scale and df, but
> note the
> >     >> comments.  You could fit a non-central t, but it would be
> unusual to do
> >     >> so.
> >     >>
> >     >>>
> >     >>> Thanks a lot!!
> >     >>>
> >     >>> Kate