How Point Statistics works
The Point Statistics tool calculates statistics on point features that fall in the neighborhood around each output raster cell. It is similar to the Focal Statistics tool except that it operates directly on the point features instead of on a raster. One of the advantages of operating directly on the features is that points are not lost in converting to a raster if they are too close together.
There are four defined neighborhood shapes that Point Statistics can calculate the statistics for. Only with the Focal Statistics tool can custom neighborhood shapes be defined.
The neighborhood shapes are annulus, circle, rectangle, and wedge. Each shape is defined by several parameters, as illustrated below:
The default neighborhood is a square with width and height of three cell units.