Good morning,

what about creating a buffer with a distance of your choice and counting the
points inside the buffer (count points inside polygon)? If you dissolve the
buffers, you should get the sum of accidents in a range defined by you
buffer distance. That could help in case your accident points have not
exactly the same coordinates although beeing very close. 

For visualisation you could then use either the buffer area (e.g. classified
with colours) or points with the sum of accidents from centroids of the
buffers (e.g. symbol sizes). 

What you want to do, seems to be a hotspot analysis that could be solved
with CrimeStat ( Wikipedia <https://en.wikipedia.org/wiki/CrimeStat>  , 
Official Website <http://www.icpsr.umich.edu/CrimeStat>  ) ...

Regards, Christine



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