Make KDE a distribution and implement other Distributions method

[matbesancon]

It would be nice to have:

• cdf using QuadGK? Or StatsBase.ecdf?
• quantile using cdf with bijection method

[tbeason]

I'm going to bump this thread. In addition to pdf, shouldn't other functions like mean, std, quantile, cdf, etc... be supported as well?

[mkborregaard]

Yes this sounds like an obviously good improvement.

[ClaudMor]

Yes, it would also be nice to have a rand method.

[Yuan-Ru-Lin]

Also loglikelihood for whoever needs to perform maximum-likelihood estimation with the resulting KDE.

[jaksle]

I was just looking at the internals of this library, checking other things and I noticed this. Unfortunately, KernelDensity.jl was not designed with such features in mind. It does not store information required to effectively calculate kernel-based features other than the pdf.

What one can do is to introduce a new interface which does store it, make a new type like KernelEstimate <: Distribution which stops one step before calculating the pdf and stores all the parameters of the fit. Perhaps it can be done even better, as I see Distributions.jl has MixtureModel implemented and kde is just a fitted mixture. I'll think about this.

[alonsoC1s]

Would implementing the basic interface for a Sampleable from Distributions.jl be feasible? It would be nice to draw sampes with rand as @ClaudMor mentioned. As far as I can tell, it only requieres extending a few methods

[jaksle]

@alonsoC1s Alas, no. The reason is this library has a bad structure. To sample from the KDE you need the parameters of the fit. Here, they are calculated inside algorithm, but the are not stored nor returned. The only thing it stores are the values of estimated pdf at discrete set of points.

You can sample from that, but I would not recommend it, it would be an ugly approximation prone to strange errors.