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# Directional Distribution (Standard Deviational Ellipse) (Spatial Statistics)

Release 9.2

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Measures whether a distribution of features exhibits a directional trend (whether features are farther from a specified point in one direction than in another direction).

Illustration

Usage tips

• The standard ellipse calculation may be based on an optional weight field.

• Standard Deviational Ellipse creates a new feature class containing an elliptical polygon. The attribute values for these ellipse polygons include two standard distances (long and short axes) and the orientation of the ellipse.

• If the underlying pattern in the data is normally distributed about the mean, the one standard deviation ellipse polygon will cover approximately 68 percent of the features in the cluster. Two standard deviations will contain approximately 95 percent of the features, and three standard deviations will cover approximately 99 percent of the features in the cluster.

• The following fields are added to the output ellipse feature class to store ellipse information: CenterX stores the x coordinate of the center of the ellipse, CenterY stores the y coordinate of the center of the ellipse, XStdDist stores the standard distance in the x direction, and YStdDist stores the standard distance in the y direction and Rotation which stores the rotation of the ellipse (if you specify a case field, it is also included in the output feature class).

• The value in the Rotation field represents the rotation of the long axis measured clockwise from noon.

• If a case field is specified, then the input features are grouped according to case field values. A mean center is calculated from the average x and y values for the centroids in each group.

• For line and polygon features, feature centroids are used in the computations.

• Calculations are based on either Euclidean or Manhattan distance and require projected data to accurately measure distances.

• Current map layers may be used to define the input feature class. When using layers, only the currently selected features are used in the Central Feature operation.

• The following environment settings affect this tool: Cluster Tolerance, Extent, M Domain, Configuration Keyword, Coordinate System, Output has M Values, Output Spatial Grid, Output has Z Values, Default Z Value, Output XY Domain, and Output Z Domain.

Command line syntax
An overview of the Command Line window
DirectionalDistribution_stats <Input_Feature_Class> <Output_Ellipse_Feature_Class> <1 Standard Deviation | 2 Standard Deviations | 3 Standard Deviations> {Weight_Field} {Case_Field}

 Parameter Explanation Data Type A feature class containing a distribution of features for which the standard deviational ellipse will be calculated. Feature Layer A polygon feature class that will contain an ellipse for each input mean center point. Each ellipse graphically portrays the directional trend (if any) of data values around its associated center point. Feature Class <1 Standard Deviation | 2 Standard Deviations | 3 Standard Deviations> The size of output ellipses in standard deviations. The default ellipse size is 1; valid choices are 1, 2, or 3 standard deviations. String {Weight_Field} The numeric field used to weight locations according to their relative importance. Field {Case_Field} Field used to group features for separate directional distribution calculations. The case field can be of numeric, date, or string type. Field
Data types for geoprocessing tool parameters

### Command line example

```workspace e:\project93\data
DirectionalDistribution assault.shp assault_ellipse.shp '1 Standard Deviation' # TYPE```

Scripting syntax
About getting started with writing geoprocessing scripts
DirectionalDistribution_stats (Input_Feature_Class, Output_Ellipse_Feature_Class, Ellipse_Size, Weight_Field, Case_Field)

 Parameter Explanation Data Type Input_Feature_Class (Required) A feature class containing a distribution of features for which the standard deviational ellipse will be calculated. Feature Layer Output_Ellipse_Feature_Class (Required) A polygon feature class that will contain an ellipse for each input mean center point. Each ellipse graphically portrays the directional trend (if any) of data values around its associated center point. Feature Class Ellipse_Size (Required) The size of output ellipses in standard deviations. The default ellipse size is 1; valid choices are 1, 2, or 3 standard deviations. String Weight_Field (Optional) The numeric field used to weight locations according to their relative importance. Field Case_Field (Optional) Field used to group features for separate directional distribution calculations. The case field can be of numeric, date, or string type. Field

Data types for geoprocessing tool parameters

### Script example

```# Measure the geographic distribution of auto thefts
# Import system modules
import arcgisscripting

# Create the Geoprocessor object
gp = arcgisscripting.create()

# Local variables...
workspace = "C:/chris/data/"
auto_theft_locations = "AutoTheft.shp"
auto_theft_sd = "auto_theft_SD.shp"
auto_theft_se = "auto_theft_SE.shp"
auto_theft_ldm = "auto_theft_LDM.shp"

try:
# Set the workspace (to avoid having to type in the full path to the data every time)
gp.Workspace = workspace

# Process: Standard Distance of auto theft locations...
gp.StandardDistance_stats(auto_theft_locations, auto_theft_sd, "1 Standard Deviation", "#", "#")

# Process: Directional Distribution (Standard Deviational Ellipse) of auto theft locations...
gp.DirectionalDistribution_stats(auto_theft_locations, auto_theft_se, "1 Standard Deviation", "#", "#")

# Process: Linear Directional Mean of auto thefts...