Asymptotic moments of near–neighbour distance distributions

Let C be a compact convex body in R⊃m and consider a set of points selected at random from C according to some well–behaved sampling distribution. We obtain an asymptotic expression for the positive moments of the kth near–neighbour distance distribution as the number of points increases to infinity.

[1]  A. J. Jones,et al.  A proof of the Gamma test , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[2]  O. C. Martin,et al.  Scaling Universalities ofkth-Nearest Neighbor Distances on Closed Manifolds , 1998 .