Difference between revisions of "Manuals/calci/KFUNCTION"
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*The K-Function is given as : | *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> | <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] | ||
Revision as of 13:45, 14 December 2016
KFUNCTION (Number)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Number} is any real number.
Description
- This function shows the value of the K function.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 :
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} represents the total area of the features and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.
Examples
- KFUNCTION(5) = 27648
- KFUNCTION(5) = 2.157794122294186e+34
- KFUNCTION(6.453) = 86400000