[R] Doubt about Student t distribution simulation

[Jose Claudio Faria]

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: joseclaudio.faria em terra.com.br
        jc_faria em uesc.br
        jc_faria em uol.com.br

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: r-help-bounces em stat.math.ethz.ch 
>> [mailto:r-help-bounces em stat.math.ethz.ch] On Behalf Of Jose 
>> Claudio Faria
>> Sent: Friday, August 04, 2006 3:09 PM
>> To: R-help em 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: joseclaudio.faria em terra.com.br
>>         jc_faria em uesc.br
>>         jc_faria em uol.com.br
>>
>> ______________________________________________
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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.
> 
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