[R] MLE for noncentral t distribution

[Spencer Graves]

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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