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 <[EMAIL PROTECTED]>
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" <[EMAIL PROTECTED]>
k> To: "kate" <[EMAIL PROTECTED]>
k> Cc: <r-help@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
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