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 ...) > -- > 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 > -- O__ ---- Peter Dalgaard Ă˜ster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 ______________________________________________ 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