Dear List, I am not sure how should i optimize a log-likelihood numerically: Here is a Text book example from Statistical Inference by George Casella, 2nd Edition Casella and Berger, Roger L. Berger (2002, pp. 355, ex. 7.4 # 7.2.b):
data = x = c(20.0, 23.9, 20.9, 23.8, 25.0, 24.0, 21.7, 23.8, 22.8, 23.1, 23.1, 23.5, 23.0, 23.0) n <- length(x) # likelihood from a 2 parameter Gamma(alpha, beta), both unknown llk = -n*log(gamma(alpha)) - n*alpha*log(beta) + (alpha - 1)*(sum(log(x))) - (sum(x))/beta # analytic 1st derivative solution w.r.t alpha, assuming beta known # by putting MLE of beta = sum(x)/(n*alpha) # (to simplify as far as possible analytically) llk.1st = - n*digamma(alpha) -n*(log(sum(x)/(n*alpha))+1) + (sum(log(x))) It feels like i should use nls(... , trace=T, start=c(alpha=...),nls.control(maxiter=100,tol=.1)) but not sure "how". Can anyone provide me hint? Thank you for your time. Ehsan http://www.youtube.com/profile_play_list?user=wildsc0p > R.Version() $platform [1] "i386-pc-mingw32" $arch [1] "i386" $os [1] "mingw32" $system [1] "i386, mingw32" $status [1] "" $major [1] "2" $minor [1] "6.1" $year [1] "2007" $month [1] "11" $day [1] "26" $`svn rev` [1] "43537" $language [1] "R" $version.string [1] "R version 2.6.1 (2007-11-26)" ____________________________________________________________________________________ Be a better friend, newshound, and ______________________________________________ R-help@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.
