Available with Spatial Analyst license.
Available with Image Analyst license.
Overview
Calculates statistics on the cells within a neighborhood around each cell of an input raster. Several shapes of neighborhood are available.
Notes
If the input raster is of floatingpoint type, only the Mean, Maximum, Median, Minimum, Percentile, Range, Standard Deviation, and Sum statistics are available.
When a circular, annulusshaped, or wedgeshaped neighborhood is specified, some of the outer diagonal cells may not be considered in the calculations since the center of the cell must be encompassed within the neighborhood.
Input NoData cells may receive a value in the output if the Ignore NoData in calculations option is checked, provided at least one cell within the neighborhood has a valid value.
Parameters
Parameter name  Description 

Raster (Required)  The input raster. 
Statistics Type  The statistic type to be calculated.
If the input raster is floating point, only the Mean, Maximum, Median, Minimum, Percentile, Range, Standard Deviation, and Sum statistic types are available. For Mean, Median, Percentile, and Standard Deviation, the output is always floating point. The default statistic type is Mean. 
Neighborhood  The shape of the area around each cell used to calculate the statistic. Each neighborhood has additional parameters with which to define the shape.
The Irregular neighborhood allows you to specify an irregularly shaped neighborhood around the processing cell. Use the Neighborhood values table to define the shape of the neighborhood kernel. A value of 0 for a cell position indicates that the cell is not part of the neighborhood, and will not be used for processing. A value of 1 indicates that its corresponding cell (and value) is a member of the neighborhood. The Weight neighborhood is similar to the Irregular neighborhood type, in that it allows you to define an irregular neighborhood around the processing cell, but it additionally allows you to apply weights to the input values. The values in the weight kernel specify which cell positions should be included within the neighborhood and the weights by which they will be multiplied. Use a value of 0 to exclude a cell from processing. Positive, negative, and decimal values are all valid options to use as a weight. Note:For the Weight neighborhood type, only the Mean, Standard Deviation, or Sum statistics are supported. 
Ignore NoData in calculations  Denotes whether NoData values are ignored by the statistic calculation.

Percentile Value  Denotes which percentile to calculate when Percentile is selected as the statistics type. The default is 90, for the 90th percentile. The values can range from 0 through 100. The 0th percentile is essentially equivalent to the Minimum statistic, and the 100th percentile is equivalent to Maximum, with the exception that the result will be floating point. A value of 50 will essentially produce the same result as the Median statistic. 
Using kernel files
For the Irregular and Weight neighborhoods, you can save a custom kernel as a text file for later use.
After specifying the width and height, and entering the neighborhood values, use the Save As button to export it to an ASCII text file through the Save Neighborhood Kernel File dialog box. Use the Browse button to open the Input Neighborhood Kernel File dialog box to browse to and specify an existing kernel file to load.
The format of the file is the same as that of the kernel files used in the Focal Statistics geoprocessing tool. The first line records the width and height of the kernel neighborhood. Then each row of text represents the value of that location in the kernel. For the Irregular neighborhood type, values of 0 and 1 determine which cells will participate in the statistic calculation. A value of 0 means the corresponding location in the neighborhood will be excluded in the calculation of the statistic, and 1 means that location will be included. The Weight neighborhood not only identifies which cell positions should be included within the neighborhood, but also the weights by which the values at those locations will be multiplied.
The Weight neighborhood is only available for the Mean, Standard Deviation, and Sum statistics types.