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.