- airy(x) :
The Airy function Ai(x)
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The Airy function Ai(x) is the solution to the
differential equation y'' - xy = 0 and is of
particular importance when solving differential
equations in WKB approximation.
- smooth kdensity
and smooth cumulative
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The smooth kdensity algorithm calculates a
Gaussian kernel density estimate for a data set. (The
bandwidth of the smoothing kernel can be set through an
optional parameter, otherwise the "Gaussian" default is
used.) A kernel density estimate is a smooth curve similar
to a histogram. (See figures on the left.)
The smooth cumulative algorithm calculates the
empirical distribution function for a data set. (See
figures on the right.)
In the figures below, the raw data set is shown as a
jitter plot in red. A conventional histogram is shown
in green. The kernel density estimate and the cumulative
distribution function are shown as smooth curves.
| Kernel Density Estimation |
Cumulative Distribution Function |
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- dgrid3d gauss
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Gnuplot's dgrid3d mode allows to create a smooth
surface from a set of points. The points do not necessarily
have to be on a regular grid (although they are in the example
shown below).
The "classic" smoothing approximation ("qnorm mode") had some
peculiarities. In particular it tended to overemphasize the
neighbourhood of the data points. (See figures on the left.)
I added some other smoothing kernels to the existing dgrid3d
infrastructure, of which the Gaussian kernel is probably the
most versatile. It leads to overall smoother surfaces and allows
for better control of the range of the smoothing kernel.
(See figures on the right.)
| qnorm Smoothing (old) |
Gaussian Kernel Smoothing (new) |
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