I have some data which I wish to estimate the marginal distribution of. I have no real idea what parametric distribution would be suitable, so was planning on fitting a non-parametric (probably kernel) density estimate to the data.
However, there are two complications
1) The data has a hard threshold at $0$
2) The data is mostly clumped around zero -- it is probably fair to say that it is a mix of two distributions, one being almost a delta at $0$, and the other being a strictly positive distribution with a long tail.
I know of some methods to deal with 1), but the simple methods I have used (reflection kernels) lead to unsatisfactory results near zero. I don't really know what to do about 2).
What is the state of the art for this kind of problem? Maybe an R-package that implements something I could try out?
Happy to give an example of the data, but I'm not sure the best way to do this. Let me know and I can edit the question.
EDIT: I tried the logspline idea - with and without removing the zeros (I actually removed all values very close to zero, $<0.05$). For interest sake, the result without removing the zeros is:
And with the zeros removed:
It looks like that with the zeros removed, an exponential distribution might fit fairly well.