StatsKDE
StatsKDE [flags] srcWave
StatsKDE can be used to estimate a PDF from original data distribution. Unlike histograms, this method produces a smooth result as it constructs the PDF from a normalized superposition of kernel functions.
The StatsKDE operation was added in Igor Pro 7.00.
Flags
| /BWM=m | Sets the bandwidth selection method. | ||||||||||||
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| /DEST=destWave | |||||||||||||
| Specifies the output destination. Creates a real wave reference for the destination wave in a user function. See Automatic Creation of WAVE References for details. | |||||||||||||
| /FREE | Makes the destination wave (specified by /DEST) a free wave. | ||||||||||||
| /H=bw | Specifies a fixed user-defined bandwidth. | ||||||||||||
| /KT=kernel | Specifies the kernel type. | ||||||||||||
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| /Q | No results printed in the history area. In the case of univariate KDE this flags suppresses the printing of the bandwidth value. | ||||||||||||
| /S={x0,dx,xn} | Specifies the range of the output starting from x=x0 to x=xn in increments of dx . | ||||||||||||
| /Z | Ignores errors. V_flag is set to zero if there are no errors. | ||||||||||||
Details
StatsKDE estimates the PDF of a distribution of values using a smoothing kernel and a bandwidth parameter which affects the degree of smoothing.
Theory suggests that the Epanechnikov kernel is the most efficient but many expressions for the optimal bandwidth are derived for the Gaussian kernel. If srcWave contains N points and the requested output (/S flag) has M points then the computational complexity is O(NM). For large problems it may be beneficial to use the Gaussian kernel via the FastGaussTransform operation.
References
Wand M.P. and Jones M.C. (1995) Monographs on Statistics and Applied Probability, London: Chapman and Hall
Bowman, A.W., and Azzalini, A. (1997), Applied Smoothing Techniques for Data Analysis, London: Oxford University Press.