REMARK ON THE PALM INTENSITY OF
NEYMAN-SCOTT CLUSTER POINT PROCESSES
Abstract. The present paper is concerned with notes on the Palm intensity of Neyman-Scott cluster point processes. The Palm intensity is known as the most important and informative second-order characteristic that plays a role of a configurational criterion for point patterns. It is remarkable that its pole at the origin and range of correlation play some intrinsic roles in the point pattern analysis. However, their generic forms cannot be derived due to the inability to explicitly describe the Palm intensity except in typical cluster point processes. This paper provides a sufficient condition for the existence of the pole and a bound on the range of correlation for more general cluster point processes. As applications of our results, we give an exact formula for a variance-area curve of the Neyman-Scott cluster point processes and a remark on a sufficient condition for a Neyman-Scott cluster point process with uniformly bounded diameter to be a connected component Markov point process. The current results play a key role in the identification problem on a superposed Neyman-Scott cluster point process model due to the Palm intensity, which is the most significant pragmatic contribution made in this paper.
AMS Subject classification: 60G55, 60D05


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DOI: 10.12732/ijam.v26i4.3

Volume: 26
Issue: 4
Year: 2013