From: Spencer Graves <spencer.graves_at_pdf.com>

Date: Fri, 09 May 2008 07:32:47 -0700

R-help_at_r-project.org mailing list

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 - 16:03:36 GMT

Date: Fri, 09 May 2008 07:32:47 -0700

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@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
**>
**> ______________________________________________
**> R-help_at_r-project.org mailing list
**> 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.
**>
*

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