You are probably making some mistake in
your simulations. I am getting answers
that seem to make sense. Here is my code:
----- Original Message -----
From: "Lambert.Winnie" <lambert.winnie@ensco.com>
Date: Wednesday, May 21, 2003 10:19 am
Subject: [S] FW: Gumbel Distribution pdf
> All,
>
> This is a non-SPLUS related stats question from a co-worker. Would
> anyone like to tackle this? Thanks.
>
> -----Original Message-----
> From: Short.Dave
> Sent: Monday, May 19, 2003 11:03 AM
> To: Lambert.Winnie
> Subject: Gumbel Distribution pdf
>
>
> Winnie,
>
> I have a question about the Gumbel distribution that may
> require the
> expertise of the S-PLUS community.
>
> If I assume an underlying Gaussian process with mean=mu and
> standarddeviation=sigma, and look at the
> theoretical distribution of maxima drawn from samples comprised of a
> large number of realizations of the process,
> the Gumbel pdf is the answer, according to my understanding.
>
> The resulting Gumbel pdf can be derived from the parameters of the
> Gaussian process, mu and sigma.
>
> What puzzles me is that the mode of the resulting Gubel pdf
> appearsto be equal to mu, the mean of the
> underlying Gaussian process, and that there is a non-negligible
> probability that maximum from a large sample
> of the Gaussian process will be less than its average value. This
> seemscounter-intuitive. I would have thought that the maximum
> of a large sample from the process would almost always come from the
> upper tail of the process, well above the mean.
>
> Perhaps I have misunderstood something.
>
> Any comments or suggestions that you or your colleagues may have are
> most welcome.
>
> Many thanks,
>
> Dave
>
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