What would be the expected value of distances to the nearest neighbor in a set of points in 2-dim space that have a clustered (not random) spatial distribution? If the distribution is random the expected value would be: 0.5/sqrt(lambda), where lambda is the density of points.

I've read that a Poisson distribution which mean is itself gamma distributed with shape=k (clustering value) and scale=lambda/k, can be used to generate clustered spatial patterns. Simulations of this method are easy to do (and it works), but how can I obtain an expression for the expected value (and maybe other momenta) of such combined distribution?


Depends on your assumption on the data. What is "clustered"?

And what is "near"?

E.g. if "clustered" means I'm drawing a 0 with p, and a 1 with 1-p, then the expected value, then the expected value of the 1-nearest neighbor distance quickly goes to 0.

Now if you assume your data has some Gaussian error, there is an expected deviation hidden in that model...


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