kth distance distributions for generalized Gauss-Poisson process in Rn

Abstract For a point process (PP), the k th contact distance refers to the distance of k th closest point from an arbitrary location and the k th nearest neighbor distance refers to the distance of k th nearest neighbor from an arbitrary point of the PP. We consider the generalized n -dimensional Gauss-Poisson process and derive the closed-form expressions for the cumulative distribution functions (CDFs) of these two distances for the general k . We also validate our analysis via numerical simulations and provide various insights using the presented analysis.

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