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Locations of the 1854 London cholera outbreak near Golden Square

Locations of the 1854 London cholera outbreak near Golden Square in the observation region GeoBoundsRegion[{{51.51065909836119`, 51.51581097178905`}, {-0.14008439736259973`, -0.13222907147321172`}}], annotated with marks including the number of cases, distance (in meters) to the contaminated Broad Street water pump, distance (in meters) to a non-Broad Street pump, and whether or not the Broad Street pump was the closest pump.

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Summary of the spatial point data:

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Plot the locations:

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Visualize the number of cases per location with information whether the contaminated pump was the closest:

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Compute probability of finding a point within given radius of an existing point - NearestNeighborG is the CDF of the nearest neighbor distribution:

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NearestNeighborG as the CDF of nearest neighbor distribution can be used to compute the mean distance between a typical point and its nearest neighbor - the mean of a positive support distribution can be approximated via a Riemann sum of 1- CDF. To use Riemann approximation create the partition of the support interval from 0 to *maxR* into 100 parts and compute the value of the NearestNeighborG at the middle of each subinterval:

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Now compute the Riemann sum to find the mean distance between a typical point and its nearest neighbor:

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Test for complete spacial randomness:

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Gosia Konwerska, "Sample Data: London Cholera" from the Wolfram Data Repository (2022)