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

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.