How is kernel density estimation for points converted to area units in ArcGIS

[erichfisher]

Does anyone know how ArcGIS converts the kernel density estimation to area units?  The help menu simple says that "the calculated density for the cell is multiplied by the appropriate factor."

Thanks,

Erich

[DanPatterson_Retired]

Your data are projected, I hope, therefore you know your area units, but more information is in the help files depending on what you are applying kernel density too, plus more information on the inner workings

Kernel Density—Help | ArcGIS for Desktop

Differences between point, line, and kernel density—Help | ArcGIS for Desktop

How Kernel Density works—Help | ArcGIS for Desktop

[erichfisher]

Hi Dan,

Thanks for the response. Yes, the data are projected and I've also read the help menus, scouted the internet, etc thoroughly.  However, there is no information on how the data are converted from the kernel density estimation to area units.  The help menu only says this:

"If an area unit is selected, the calculated density for the cell is multiplied by the appropriate factor before it is written to the output raster."

What I would like to know is what is meant by the "appropriate factor?"

For example, if I were to use SciPy to calculate kernel density using Scott's rule (ArcGIS uses Silverman's) then how do I convert the those kernel density estimations into area units like ArcGIS?

[DanPatterson_Retired]

from the 2nd link, my reading would be metric if you are using most projected coordinate systems (ie meters for units).  With the caveat in the 2nd paragraph since observations per square meter would be pretty ridiculous, so it is scaled up to a km^2. 

Silverman's reference can be found in many links like  https://ned.ipac.caltech.edu/level5/March02/Silverman/paper.pdf   

Density Estimation for Statistics and Data Analysis -B.W. Silverman

but the equation numbers don't match up

but you can go to this weird link and see it

https://books.google.ca/books?id=e-xsrjsL7WkC&printsec=frontcover&hl=en#v=onepage&q&f=false on page 76 as referenced here which Bill Huber discusses here Density

By default, a unit is selected based on the linear unit of the projection definition of the input point feature data or as otherwise specified in the output coordinate system environment setting. If an area unit is selected, the calculated density for the cell is multiplied by the appropriate factor before it is written to the output raster.

For example, if the input units are meters, the output area units will default to square kilometers. Comparing a unit scale factor of meters to kilometers will result in the values being different by a multiplier of 1,000,000 (1,000 meters x 1,000 meters).