# [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

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

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)) }

```      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
mails: joseclaudio.faria@terra.com.br

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

______________________________________________
```
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