From: Martin Maechler <maechler_at_stat.math.ethz.ch>

Date: Fri, 09 May 2008 08:37:18 +0200

>>> 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":
*

* >>>
*

* >>> 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?
*

>>> library(MASS)

>>> ?fitdistr

* >>>
*

* >>> Thanks a lot!!
*

* >>>
*

* >>> Kate
*

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Fri 09 May 2008 - 06:39:47 GMT

Date: Fri, 09 May 2008 08:37:18 +0200

>>>>> "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

>> >> So you mean 'non-central'? See ?dt. >>

>>> I found an example to find MLE for gamma distribution from "fitting

>> >> 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. >>

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