[R] MLE for noncentral t distribution

[kate]

In my data,  sample mean =-0.3 and the histogram looks like t distribution; 
therefore, I thought non-central t distribution may be a good fit. Anyway, I 
try t distribution to get MLE. I found some warnings as follows; besides, I 
got three parameter estimators: m=0.23, s=4.04, df=1.66. I want to simulate 
the data with sample size 236 and this parameter estimates. Is the command 
rt(236, df=1.66)? Where should I put m and s when I do simulation?

       m           s          df
  0.2340746   4.0447124   1.6614823
 (0.3430796) (0.4158891) (0.2638703)
Warning messages:
1: In dt(x, df, log) : generates NaNs
2: In dt(x, df, log) : generates NaNs
3: In dt(x, df, log) :generates NaNs
4: In log(s) : generates NaNs
5: In dt(x, df, log) : generates NaNs
6: In dt(x, df, log) : generates NaNs

Thanks a lot,

Kate

----- Original Message ----- 
From: "Prof Brian Ripley" <ripley at stats.ox.ac.uk>
To: "kate" <yhsu6 at uiuc.edu>
Cc: <r-help at r-project.org>
Sent: Thursday, May 08, 2008 10:02 AM
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
>> [[alternative HTML version deleted]]
>>
>> ______________________________________________
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>> PLEASE do read the posting guide 
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>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> -- 
> Brian D. Ripley,                  ripley at stats.ox.ac.uk
> Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
> University of Oxford,             Tel:  +44 1865 272861 (self)
> 1 South Parks Road,                     +44 1865 272866 (PA)
> Oxford OX1 3TG, UK                Fax:  +44 1865 272595