# Mean of nearest neighbour distance in a clustered distribution

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?