[R] MLE for noncentral t distribution

[Martin Maechler]

>>>>> "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