KERNEL DENSITY WIDTHName:
where K is the kernel function h is the smoothing parameter or window width.
This command sets the value of the window width, h.
Following the recommendation of Silverman (1986), DATAPLOT uses a default width of
where s is the sample standard deviation and IQ is the sample interquartile range. Silverman provides justification for this choice. Basically, it should perform reasonably for a wide variety of distributions. Note that the optimal width depends on the underlying function, which is what we are trying to estimate.
If the underlying data is in fact normally distributed, then Silverman (1986) shows that the optimal width is
where n is the number of points in the raw data and s is the sample standard deviation of the raw data.
It may be worthwhile to generate the density curve using several different values for the width. Silverman also recommends trying to transform skewed data sets to be symmetric.
where <value> is a number or parameter that specifies the desired width.
The width should be strictly positive.
KERNEL DENSITY WIDTH 1.2
LET S = STANDARD DEVIATION Y