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

Robin Hankin r.hankin at soc.soton.ac.uk
Thu Dec 2 13:22:29 CET 2004

```[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.

Kia Ora

> Best wishes,
> Ted.
>
>
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> Date: 02-Dec-04                                       Time: 11:30:01
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