# Re: [R] MLE for noncentral t distribution

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Thu, 08 May 2008 10:46:23 -0400

On 5/8/2008 10:34 AM, 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.
>
> 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?

dt() has a non-centrality parameter and a log parameter, so it would simply be

ll <- function(x, ncp, df) sum(dt(x, ncp=ncp, df=df, log=TRUE))

Make sure you convert mu into the ncp properly; the man page says how ncp is interpreted.

Duncan Murdoch

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