Standard Article

Ripley's K Function

Natural Resources and Agriculture

  1. Philip M. Dixon

Published Online: 15 JAN 2013

DOI: 10.1002/9780470057339.var046.pub2

Encyclopedia of Environmetrics

Encyclopedia of Environmetrics

How to Cite

Dixon, P. M. 2013. Ripley's K Function . Encyclopedia of Environmetrics. 5.

Author Information

  1. Iowa State University, Ames, IA, USA

Publication History

  1. Published Online: 15 JAN 2013


Ripley's K function summarizes spatial point process data. It can be used to describe a set of locations, test hypotheses about patterns, and estimate parameters in a spatial point process model. For a stationary point process, K(t) is the expected number of additional points within distance t of a focal point divided by the intensity of the process. A univariate version is used for one set of locations and a multivariate version is used when points can be labeled by a small number of groups. This article reviews the properties of Ripley's K function and two related functions, then illustrates the computation and interpretation using data on the locations of trees in a swamp hardwood forest.


  • spatial point process;
  • spatial point pattern;
  • clustering;
  • spatial scale;
  • spatial segregation;
  • edge effect corrections