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Abstract:
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Clusters of different objects are of great interest in many fields, such as agriculture and ecology. One kind of clustering methods is very different from the traditional statistical clustering analysis, which is based on discrete data points. This method of clustering defines clusters as the connected areas where a well-defined spatial random field is above certain threshold. The statistical properties, especially the distributional properties, of the defined clusters are vital for the studies of related fields. However, the available statistical techniques for analyzing clustering models are not applicable to these problems. We study the distribution properties of the clusters by defining a distribution function of the clusters rigorously, and providing methods to estimate the spatial distribution function. Our results are illustrated by numerical experiments and an application to a real world problem.
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