Dears John, Peter and Sundar, Many thanks for the quick answers!!!
.. and sorry for all.. []s ___ Jose Claudio Faria Brasil/Bahia/Ilheus/UESC/DCET Estatística Experimental/Prof. Adjunto mails: [EMAIL PROTECTED] [EMAIL PROTECTED] [EMAIL PROTECTED] John Fox escreveu: > Dear Jose, > > The problem is that you're using the population standard deviation (sigma) > rather than the sample SD of each sample [i.e., t[i] = (mean(amo.i) - mu) / > (sd(amo.i) / sqrt(n)) ], so your values should be normally distributed, as > they appear to be. > > A couple of smaller points: (1) Even after this correction, you're sampling > from a discrete population (albeit with replacement) and so the values won't > be exactly t-distributed. You could draw the samples directly from N(mu, > sigma) instead. (2) It would be preferable to make a quantile-comparison > plot against the t-distribution, since you'd get a better picture of what's > going on in the tails. > > I hope this helps, > John > > -------------------------------- > John Fox > Department of Sociology > McMaster University > Hamilton, Ontario > Canada L8S 4M4 > 905-525-9140x23604 > http://socserv.mcmaster.ca/jfox > -------------------------------- > >> -----Original Message----- >> From: [EMAIL PROTECTED] >> [mailto:[EMAIL PROTECTED] On Behalf Of Jose >> Claudio Faria >> Sent: Friday, August 04, 2006 3:09 PM >> To: R-help@stat.math.ethz.ch >> Subject: [R] Doubt about Student t distribution simulation >> >> 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 >> Estatística 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. > > > Esta mensagem foi verificada pelo E-mail Protegido Terra. > Scan engine: McAfee VirusScan / Atualizado em 04/08/2006 / Versão: 4.4.00/4822 > Proteja o seu e-mail Terra: http://mail.terra.com.br/ > > > ______________________________________________ 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.