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Short distances, flat triangles and Poisson limits

  • Bernard Silverman (a1) and Tim Brown (a2)


Motivated by problems in the analysis of spatial data, we prove some general Poisson limit theorems for the U-statistics of Hoeffding (1948). The theorems are applied to tests of clustering or collinearities in plane data; nearest neighbour distances are also considered.


Corresponding author

Now at the University of Bath.


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Brown, T. C. and Silverman, B. W. (1979) Rates of Poisson convergence for U-statistics, J. Appl. Prob. To appear.
Hoeffding, W. (1948) A class of statistics with asymptotically normal distribution. Ann. Math. Statist. 19, 293325.
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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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