Dear R list, I would like to illustrate the origin of the Student t distribution using R.
So, if (sample.mean - pop.mean) / standard.error(sample.mean) has t distribution with (sample.size - 1) degree free, what is wrong with the simulation below? I think that the theoretical curve should agree with the relative frequencies of the t values calculated: #== begin options===== # parameters mu = 10 sigma = 5 # size of sample n = 3 # repetitions nsim = 10000 # histogram parameter nchist = 150 #== end options======= t = numeric() pop = rnorm(10000, mean = mu, sd = sigma) for (i in 1:nsim) { amo.i = sample(pop, n, replace = TRUE) t[i] = (mean(amo.i) - mu) / (sigma / sqrt(n)) } win.graph(w = 5, h = 7) split.screen(c(2,1)) screen(1) hist(t, main = "histogram", breaks = nchist, col = "lightgray", xlab = '', ylab = "Fi", font.lab = 2, font = 2) screen(2) hist(t, probability = T, main = 'f.d.p and histogram', breaks = nchist, col = 'lightgray', xlab = 't', ylab = 'f(t)', font.lab = 2, font = 2) x = t curve(dt(x, df = n-1), add = T, col = "red", lwd = 2) Many thanks for any help, ___ Jose Claudio Faria Brasil/Bahia/Ilheus/UESC/DCET EstatÃstica Experimental/Prof. Adjunto mails: [EMAIL PROTECTED] [EMAIL PROTECTED] [EMAIL PROTECTED] ______________________________________________ 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 and provide commented, minimal, self-contained, reproducible code.