# explanation notation kernel density function

Question asked by geonetadmin on Feb 16, 2013
Original User: Peter_M

Hallo

I´m new in statistics and I have only basic skills in maths, I write my master thesis for the university, there I use a simple density map as I thought. But now I have to descripe the theorie behind the toolfunction :-(

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]21864[/ATTACH]

with a quadratic kernel function of these!
[ATTACH=CONFIG]21865[/ATTACH]

I´m rather new in statistics/maths and in the original literature it´s seems that it is assumed that verybody 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 X[SUB]1[/SUB] , ... X[SUB]n[/SUB]
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[SUP]d[/SUP] = ?
x = ?
X[SUB]i[/SUB] = ?
if x[SUP]T[/SUP]x < 1 = ?

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

Peter