[R] Doubt about Student t distribution simulation
Peter Dalgaard
p.dalgaard at biostat.ku.dk
Fri Aug 4 22:21:08 CEST 2006
Jose Claudio Faria <joseclaudio.faria at terra.com.br> writes:
> 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))
At the very least, you need a sample-based standard error: sd(amo.i),
not sigma. Also, resampling from "pop" is not really what the
t-distribution is based on, but I don't think that matters much.
> }
>
> 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: joseclaudio.faria at terra.com.br
> jc_faria at uesc.br
> jc_faria at uol.com.br
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
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> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
--
O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B
c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K
(*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk) FAX: (+45) 35327907
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