On Tue, 24 Apr 2001 19:19:02 -0500, burt <[EMAIL PROTECTED]>
wrote:
>It seems that someplace in my statistical education I read or heard one
>of my teachers make the following statement: When the occurrence of rare
>events follows a Poisson process, then a characteristic of this process
>is as follows: Usually there are long periods of time between the
>events occurring, but occasionally the event may happen several times in
>a relatively short period of time.
>Can anyone provide a reference to this???
The time between occurrences of a Poisson process has an exponential
distribution. If you look at a graph of an exponential density
function you'll see that there are a few very long time periods
between arrivals, and a lot of very short ones. It turns out that
those few long periods are sometimes very long periods, so that
looking at a time line, if you randomly pick a time, you are likely to
pick a time that's within one of those few long periods.
A sample sequence marked off on a time line tends to look like
xx x x x x x x x x x xxx x
The visual appearnce tends to look like what you mgiht expect a
non-random clumping process to look like.
Pretty much any intro applied stochatic processes textbook should talk
about this. Cinlar is one. Ross is another.
Gary Carson
http://www.garycarson.com
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