Vernalis JFreeChart-based plotting nodes version 1.30.1.v202103301200 by Vernalis (R&D), UK
This node plots a 1D Kernel density function based on an incoming data table
A variety of kernel estimators are available, as shown in the table:
|UNIFORM||K(u) = 0.5 (|u| ≤ 1), 0 (|u) > 1); aka 'Uniform' or 'Boxcar'|
|TRIANGLE||K(u) = 1-|u| (|u| ≤ 1), 0 (|u) > 1)|
|EPANECHNIKOV||K(u) = 3•(1-u²)/4 (|u| ≤ 1), 0 (|u) > 1)|
|QUARTIC||K(u) = 15•(1-u²)²/16 (|u| ≤ 1), 0 (|u) > 1)|
|TRIWEIGHT||K(u) = 35•(1-u²)³/32 (|u| ≤ 1), 0 (|u) > 1)|
|TRICUBE||K(u) = 70•(1-|u|³)³/81 (|u| ≤ 1), 0 (|u) > 1)|
|GAUSSIAN||K(u) = e^(-u²/2) / √(2π)|
|COSINUS||K(u) = (π/4)•cos(πu/2) (|u| ≤ 1), 0 (|u) > 1)|
|LOGISTIC||K(u) = 1/(e^u + 2 + e^-u)|
|SIGMOID||K(u) = 2/(π•(e^u + e^-u))|
|SILVERMAN||K(u) = 0.5•e^(-|u|/√2)•sin((|u|/√2) + (π/4))|
The bandwidth effects the 'smoothness' of the kernel density function. There are a number of methods to automatically guess a suitable bandwidth. In this node we only offer three options, as shown in the table below. For further details see the Wikipedia Multivariate Kernel Density estimation page.
The methods offered are:
|Silverman||Bandwidth is estimated using the Silverman approximation (H = stdDev * [4 / ((d + 2) * n)]^(1 / (d + 4)), where d is thenumber of dimensions and n the number of datapoints)|
|Scott||Bandwidth is estimated using the Scott approximation (H = stdDev / n^(1 / (d + 4)), where d is thenumber of dimensions and n the number of datapoints)|
|User Defined||The user specifies the bandwidth (H)|
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