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Biometrika 1968 55(1):258-260; doi:10.1093/biomet/55.1.258
© 1968 by Biometrika Trust
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MISCELLANEA

A three-dimensional cluster problem

F. D. K. ROBERTS and S. H. STOREY

University of Liverpool

The expected size of clusler in a three-dimensional Poisson ensemble is discussed. This expected size is a function of one parameter t. There exists a critical value t=t0 at which the expected cluster size becomes infinite and for t>t0 infinite clustors occur. A lower bound t0≥0.0434 and a Monte Carlo estimate t0=0.0889 are obtained. An application of this problem to a percolation process is discussed.


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