From: Gregor Gorjanc <gregor.gorjanc_at_gmail.com>

Date: Sat 11 Feb 2006 - 03:25:32 EST

*>
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*>
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> Yes....

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*> Maximizing l(lambda) is the same as maximizing
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*>
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*> sum(x)/n ln lambda - lambda
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*>
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*> Now either take the derivative and set equal to zero, or
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*>
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*> rewrite further as equivalent to
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*>
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*> ln (lambda/(sum(x)/n)) - (lambda/(sum(x)/n))
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*>
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*> and notice that ln(x) - x has a global maximum at x=1 (since ln is
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*> strictly concave and the tangent at x=1 is the line y = x - 1)
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*>
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*>
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*> (I think this is in the first 20 pages I ever read on theoretical
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*> statistics ...)
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Date: Sat 11 Feb 2006 - 03:25:32 EST

Peter Dalgaard wrote:

> Gregor Gorjanc <gregor.gorjanc@bfro.uni-lj.si> writes:

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**>
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>>Hello! >> >>I would like to get MLE for parameter lambda of Poisson distribution. I >>can use fitdistr() for this. After looking a bit into the code of this >>function I can see that value for lambda and its standard error is >>estimated via >> >>estimate <- mean(x) >>sds <- sqrt(estimate/n) >> >>Is this MLE? With my poor math/stat knowledge I thought that MLE for >>Poisson parameter is (in mixture of LaTeX code) >> >>l(\lambda|x) \propto \sum^n_{i=1}(-\lambda + x_iln(\lambda)). >> >>Is this really equal to (\sum^n_{i=1} x_i) / n

> Yes....

Thank you very much for this. It shows, how much I still need to learn.

-- Lep pozdrav / With regards, Gregor Gorjanc ---------------------------------------------------------------------- University of Ljubljana PhD student Biotechnical Faculty Zootechnical Department URI: http://www.bfro.uni-lj.si/MR/ggorjan Groblje 3 mail: gregor.gorjanc <at> bfro.uni-lj.si SI-1230 Domzale tel: +386 (0)1 72 17 861 Slovenia, Europe fax: +386 (0)1 72 17 888 ---------------------------------------------------------------------- "One must learn by doing the thing; for though you think you know it, you have no certainty until you try." Sophocles ~ 450 B.C. ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.htmlReceived on Sat Feb 11 03:30:02 2006

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