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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?

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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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