Add custom kernel density estimation #239
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This gets rid of the KernelDensity dependency. It works, but can probly be a bit more efficient.
Codecov ReportAll modified and coverable lines are covered by tests ✅
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## master #239 +/- ##
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+ Coverage 94.32% 94.42% +0.09%
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Files 35 36 +1
Lines 1568 1596 +28
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+ Hits 1479 1507 +28
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In comparison to the previous approach this give completely smooth pdf, cdf, and quantile curves. It is a bit inefficient and might be improved with interpolation in the future.
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This gets rid of the KernelDensity dependency. The main annoyance with KernelDensity was the FFTW dependency which in turn pulled in MKL.
The method used to select the bandwidth for the KDE is taken from S. J. Sheather and M. C. Jones, ‘A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation’, Journal of the Royal Statistical Society: Series B (Methodological), vol. 53, no. 3, pp. 683–690, 1991, doi: 10.1111/j.2517-6161.1991.tb01857.x.
Along with the PDF I also changed the CDF and inverse CDF. Before we used the native Julia
ecdffunction for the CDF and interpolated thequantilefrom the available data andecdfvalues, but I'm not a fan because it's not a smooth function. Now I've implemented numerical integration of the actual underlying PDF usingQuadKGfor the CDF and the inverse through root finding via Root. Two new dependencies, but they are pretty lightweight so I think its fine. The biggest benefit here is, that now the CDF and quantile are actual inverses soquantile(cdf(x) == xwhich didn't really hold before.We'll have see if we need more efficient approaches in the future, but the accuracy is of the charts in comparison to the previous implementation. I've also added docs, docstrings and more stable tests.