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Statistica Sinica 22 (2012), 1717-1736

doi:http://dx.doi.org/10.5705/ss.2010.245





A GENERALIZATION OF THE NEYMAN-SCOTT PROCESS


Chun Yip Yau and Ji Meng Loh


The Chinese University of Hong Kong and AT$\&$T Labs-Research


Abstract: In this paper we introduce a generalization of the Neyman-Scott process [#!neyman58!#] that allows for regularity in the parent process. In particular, we consider the special case where the parent process is a Strauss process with offspring points dispersed about the parent points. Such a generalization allows for point realizations that show a mix of regularity and clustering in the points. We work out a closed form approximation of the $K$ function for this model and use this to fit the model to data. The approach is illustrated by applications to the locations of a species of trees in a rainforest dataset.



Key words and phrases: Gibbs process, Neyman-Scott process, K-function, regular point process.

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