ON THE ESTIMATION OF DISTANCE DISTRIBUTION FUNCTIONS FOR POINT PROCESSES AND RANDOM SETS

Abstract

This paper discusses various estimators for the nearest neighbour distance distribution function D of a stationary point process and for the quadratic contact distribution function Hq of a stationary random closed set. It recommends the use of Hanisch's estimator of D, which is of Horvitz-Thompson type, and the minussampling estimator of Hq. This recommendation is based on simulations for Poisson processes and Boolean models.

Keywords

• contact distribution
• Horvitz-Thompson
• estimator
• minus-sampling
• nearest neighbour distance distribution