[R] Doubt about Student t distribution simulation

From: Jose Claudio Faria <joseclaudio.faria_at_terra.com.br>
Date: Sat 05 Aug 2006 - 06:09:23 EST


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: joseclaudio.faria@terra.com.br

        jc_faria@uesc.br
        jc_faria@uol.com.br

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