A Class of Local and Global K Functions and Their Exact Statistical Methods

  • Atsu Okabe
  • Barry Boots
  • Toshiaki Satoh
Part of the Advances in Spatial Science book series (ADVSPATIAL)


In 1987 Getis and Franklin introduced a technique, based on second-order methods, for quantifying clustering at various scales in mapped point patterns. Subsequently, this technique has become known as local K function analysis. In this paper we develop the local and global forms of a class of K functions and cross K functions formulated on a bounded plane that includes the technique of Getis and Franklin. Exact statistical methods are formulated or discussed and computational methods are shown for the functions.


Binomial Distribution Voronoi Diagram Algebraic Function Railway Station Local Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Atsu Okabe
    • 1
  • Barry Boots
    • 2
  • Toshiaki Satoh
    • 1
  1. 1.University of TokyoTokyoJapan
  2. 2.Wilfrid LaurierWaterlooCanada

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