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kth distance distributions for generalized Gauss-Poisson process in Rn

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  • Pandey, Kaushlendra
  • Gupta, Abhishek K.

Abstract

For a point process (PP), the kth contact distance refers to the distance of kth closest point from an arbitrary location and the kth nearest neighbor distance refers to the distance of kth 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.

Suggested Citation

  • Pandey, Kaushlendra & Gupta, Abhishek K., 2021. "kth distance distributions for generalized Gauss-Poisson process in Rn," Statistics & Probability Letters, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:stapro:v:172:y:2021:i:c:s0167715221000109
    DOI: 10.1016/j.spl.2021.109048
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    References listed on IDEAS

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    1. James P. Quirk & Rubin Saposnik, 1962. "Admissibility and Measurable Utility Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 29(2), pages 140-146.
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    1. Azimi-Abarghouyi, Seyed Mohammad & Dhillon, Harpreet S., 2024. "Matérn cluster process with holes at the cluster centers," Statistics & Probability Letters, Elsevier, vol. 204(C).

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