Dear Sundar, Try qq.plot(t, dist="t", df=n-1) from the car package, which include a 95-percent point-wise confidence envelope that helps you judge how extreme the outliers are relative to expectations.
Regards, John -------------------------------- John Fox Department of Sociology McMaster University Hamilton, Ontario Canada L8S 4M4 905-525-9140x23604 http://socserv.mcmaster.ca/jfox -------------------------------- > -----Original Message----- > From: Sundar Dorai-Raj [mailto:[EMAIL PROTECTED] > Sent: Friday, August 04, 2006 3:27 PM > To: John Fox > Cc: [EMAIL PROTECTED]; [email protected] > Subject: Re: [R] Doubt about Student t distribution simulation > > Hi, Jose/John, > > Here's an example to help Jose and highlights John's advice. > Also includes set.seed which should be included in all > simulations posted to R-help. > > set.seed(42) > mu <- 10 > sigma <- 5 > n <- 3 > nsim <- 10000 > m <- matrix(rnorm(n * nsim, mu, sigma), nsim, n) t <- > apply(m, 1, function(x) (mean(x) - mu)/(sd(x)/sqrt(n))) > > library(lattice) > qqmath(t, distribution = function(x) qt(x, n - 1), > panel = function(x, ...) { > panel.qqmath(x, col = "darkblue", ...) > panel.qqmathline(x, col = "darkred", ...) > }) > > > With n = 3, expect a few outliers. > > --sundar > > > John Fox wrote: > > 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: [email protected] > >>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 > >>EstatÃstica Experimental/Prof. Adjunto > >>mails: [EMAIL PROTECTED] > >> [EMAIL PROTECTED] > >> [EMAIL PROTECTED] > >> > >>______________________________________________ > >>[email protected] 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. > > > > > > ______________________________________________ > > [email protected] 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. ______________________________________________ [email protected] 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.
