Difference between revisions of "Manuals/calci/KFUNCTION"

Revision as of 13:45, 14 December 2016

KFUNCTION (Number)

This function shows the value of the K function.
In $KFUNCTION(Number)$ ,Number is any real number.
K function is named as Ripley's K Function.
It is defined as how the spatial clustering or dispersion of feature centroids changes when the neighborhood size changes.
When using this tool, specify the number of distances to evaluate and, optionally, a starting distance and/or distance increment.
The K-Function is given as :

$L(d)={\frac {\sqrt {A\sum _{i=1}^{n}\sum _{j=1,j\neq i}^{n}k(i,j)}}{\pi n(n-1)}}$

Where d is the distance, n is equal to the total number of features.

$A$ represents the total area of the features and $k_{i,j}$ is a weight.
If there is no edge correction, then the weight will be equal to one when the distance between i and j is less than d, and will equate to zero otherwise.

@@ Line 10: / Line 10: @@
 *The K-Function is given as :
 <math>L(d)=\frac{\sqrt{A \sum_{i=1}^n \sum_{j=1,j\neq i}^n k(i,j)}}{\pi n(n-1)}</math>
+ Where d is the distance, n is equal to the total number of features.
+*<math>A</math> represents the total area of the features and <math>k_{i,j}</math> is a weight.
+*If there is no edge correction, then the weight will be equal to one when the distance between i and j is less than d, and will equate to zero otherwise.
+==Examples==
+# KFUNCTION(5) = 27648
+# KFUNCTION(5) = 2.157794122294186e+34
+# KFUNCTION(6.453) = 86400000
+==See Also==
+*[[Manuals/calci/SUM | SUM]]
+*[[Manuals/calci/SQRT | SQRT]]
+==References==
+[http://resources.esri.com/help/9.3/arcgisdesktop/com/gp_toolref/spatial_statistics_tools/how_multi_distance_spatial_cluster_analysis_colon_ripley_s_k_function_spatial_statistics_works.htm  K Function]