# Re: [R] MLE for noncentral t distribution

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Fri, 09 May 2008 07:32:47 -0700

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@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":
> >>>
> >>> 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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