Peter Dalgaard wrote: > Gregor Gorjanc <[EMAIL PROTECTED]> writes: > > >>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.... > > Maximizing l(lambda) is the same as maximizing > > sum(x)/n ln lambda - lambda > > Now either take the derivative and set equal to zero, or > > rewrite further as equivalent to > > ln (lambda/(sum(x)/n)) - (lambda/(sum(x)/n)) > > and notice that ln(x) - x has a global maximum at x=1 (since ln is > strictly concave and the tangent at x=1 is the line y = x - 1) > > > (I think this is in the first 20 pages I ever read on theoretical > statistics ...)
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.html