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

Liaw, Andy andy_liaw at merck.com
Thu Dec 2 14:33:30 CET 2004

```> 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
> > ------------------------------ XFMail ------------------------------
> >
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > http://www.R-project.org/posting-guide.html
> >
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help