Extending Poisson Distribution to trending datasets

From: Fred Chen (flipsu5_at_comcast.net)
Date: 09/29/04 

Date: 29 Sep 2004 10:58:51 -0700

What care must I take to apply Poisson statistics to data that
normally exhibits random behavior from one data point to another, but
could reflect a systematic behavior in the big picture, i.e., exhibit
a long-term trend?

In case the Poisson assumption breaks down, what statistics can be
used for the analysis?

Thanks in advance,

Fred