topic Kernel Density algorithm in ArcGIS Spatial Analyst Questions

Kernel Density algorithm

PierreLACROIX — Wed, 14 Apr 2010 10:16:03 GMT

Hi,
Does someone know the algorithm that is used by the Spatial Analyst > Kernel function?
Thank you in advance.
Piotr

Kernel Density algorithm

PierreLACROIX — Wed, 14 Apr 2010 13:57:18 GMT

Thank you Bill, it helps me for one of the parameters.
In fact Kernel functions could be look like what is in the attached file, and I think that your answer only describes the K parameter. My question would rather be: does Spatial Analyst use a normal or a variable Kernel?
Thank you in advace.
Piotr

Kernel Density algorithm

PierreLACROIX — Thu, 15 Apr 2010 06:42:26 GMT

Thank you very much for your answer Bill, that is great.
You mean that the equation would be the first one (without the dj,k factor)? In fact, I thought that the output value was highest at the location of the point and was decreasing with increasing distance from the point, reaching zero at the Search radius distance from the point. Maybe I did missed something...
Best regards.
Piotr

Kernel Density algorithm

PierreLACROIX — Thu, 15 Apr 2010 14:38:56 GMT

ok great
thanks

Re: Kernel Density algorithm

PeterMarkus1 — Sat, 16 Feb 2013 08:29:23 GMT

I have found on the help page that arcgis use these function
http://help.arcgis.com/de/arcgisdesktop/10.0/help/index.html#/na/009z00000011000000/

A kernel function like these which I had found in the literature citation of arcgis
[ATTACH=CONFIG]21862[/ATTACH]

with a quadratic kernel function of these!
[ATTACH=CONFIG]21863[/ATTACH]

I´m rather new in statistics/maths and in the original literature it´s seems that it is assumed that everybody know the "variables" meaning or I haven´t found the whole explanation.

I know the following variables as I mean:
^f(x) = density estimator
n = a sample of observations X₁ , ... X_n
K = kernel function (K will be a radially symmetric unimodal probability density function for example a quadratic)
h = bandwidth or smoothing parameter

But is anybody here how can guess or say what the variables mean (in two or three short words please)
nh^d = ?
x = ?
X_i = ?
if x^Tx < 1 = ?

Thanks it would be great because I need it as a short explanation in my master thesis!

Peter