[R] A somewhat off the line question to a log normal distrib

[Liaw, Andy]

> From: Robin Hankin
> 
> [stuff about the CLT deleted]
> 
> >
> > So you can use R usefully to eveluate general statisical
> > issues of this kind!
> >
> 
> absolutely!  R is excellent for this sort of thing.  I use it for 
> teaching stats all the time.
> I'd say that without a tool like R you cannot learn statistics.
> 
> 
> Consider an exponential distribution, which is very skewed.
> 
> f <- function(n){mean(rexp(n))}
> 
> then f(10) gives the mean of 10 independent exponentially distributed 
> random
> variables.  Then
> 
> hist(replicate(10000,f(10)))
> 
> gives us a histogram of 10000 observations of a variable that 
> is itself 
> the mean of 10 exponential variables.  It still looks a bit 
> skew to me. 
>   Try 100 exponential variables:
> 
> hist(replicate(10000,f(100)))
> 
> Still a tiny bit skew.
> 
> 
> hist(replicate(1000,f(1000)))
> which is indistinguishable from a Gaussian.
> 
> 
> So as n -> infinity, the CLT kicks in.  But here 100 is a bit 
> less than 
> infinity and 1000 ~= infinity.
> 
> It's one thing to know a theoretical result, it's quite another to 
> verify it numerically.

... but one needs to be careful when going the other direction:  It's
dangerous to take what is seen in numerical experiments as the `truth',
without verifying it more rigorously.

Andy
 
> Kia Ora
> 
> > Best wishes,
> > Ted.
> >
> >
> > --------------------------------------------------------------------
> > E-Mail: (Ted Harding) <Ted.Harding at nessie.mcc.ac.uk>
> > Fax-to-email: +44 (0)870 094 0861  [NB: New number!]
> > Date: 02-Dec-04                                       Time: 11:30:01
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