The KDE form ()
plots a discrete Kernel Density Estimate giving a smoothed
frequency of data values along the horizontal axis,
using a fixed-width smoothing kernel.
(for a variable-bandwidth kernel, see KNN).
This is a generalisation of a histogram in which the bins are always
1 pixel wide, and a smoothing kernel is applied to each bin. The width
and shape of the kernel may be varied.
This is suitable for cases where the division into discrete bins done by a normal histogram is unnecessary or troublesome.
Note this is not a true Kernel Density Estimate, since, for performance reasons, the smoothing is applied to the (pixel-width) bins rather than to each data sample. The deviation from a true KDE caused by this quantisation will be at the pixel level, hence in most cases not visually apparent.
This form may be used in the Histogram, Plane or Time plot windows.
Example KDE plot
KDE form configuration panel
These options always appear in the form configuration panel:
sum-per-unit
and
mean
make sense,
others such as
sum
do not.
The combined values are those given by the Weight coordinate, but if no weight is supplied, a weighting of unity is assumed.
The available options are:
sum
:
the sum of all the combined values per bin
sum-per-unit
:
the sum of all the combined values per unit of bin size
count
:
the number of non-blank values per bin (weight is ignored)
count-per-unit
:
the number of non-blank values per unit of bin size
(weight is ignored)
mean
:
the mean of the combined values
median
:
the median of the combined values (may be slow)
min
: the minimum of all the combined values
max
: the maximum of all the combined values
stdev
:
the sample standard deviation of the combined values
hit
:
1 if any values present, NaN otherwise (weight is ignored)
Sliding the slider to the right makes the kernel width larger. The width in data units is shown in the text field on the right (if the X axis is logarithmic, this is a factor). Alternatively you can click the radio button near the text field, and enter the width in data units directly.
The available options are: