FW: Gumbel Distribution pdf

["Lambert.Winnie" <lambert.winnie@ensco.com>]

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 standard deviation=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 appears to 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 seems counter-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