[R] MLE for noncentral t distribution
Balzer Susanne
susanne.balzer at imr.no
Tue Oct 27 00:08:14 CET 2009
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
>
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>
> 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
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