issue_comments

I have added a test to verify that using equal weights with the different interpolation methods that this PR supports would work (i.e. would yield the same results as np.quantile, with the corresponding methods). It is skipped however because the method argument is not currently exposed in the API (it would be in future work, ideally).

@huard's latest commit modifies the algorithm so that it uses Kish's effective sample size, as described in the blog where the algorithm comes from: https://aakinshin.net/posts/kish-ess-weighted-quantiles/, which seems to solve the problem mentioned by @mathause.

Also he adds support for the interpolation types 4 to 9 (those that share a common way of computing Qp, as described here: https://en.wikipedia.org/wiki/Quantile#Estimating_quantiles_from_a_sample

@mathause About this:

I did some tries and got an unexpected result:

```python data = xr.DataArray([0, 1, 2, 3]) weights = xr.DataArray([1, 0, 1, 0]) data.weighted(weights).quantile([0.75])

np.quantile([0, 2], 0.75) ```

Can you double-check? Or do I misunderstand something?

My latest commit should fix (and test) this.

@mathause Thanks for the many excellent suggestions! After having removed the for loop the way you suggested, I tried to address this:

The algorithm is quite clever but it multiplies all elements (except 2) with 0 - this could maybe be sped up by only using the relevant elements.

At first I thought that something like this could work:

python w = np.diff(v) nz = np.nonzero(w) d2 = np.tile(data, (n, 1)) r = w[nz] * d2[nz] r = r[::2] + r[1::2]

The problem however is that it turns out that w's rows sometimes have one element only, instead of two (which is when an h coincides exactly with a weight value, instead of lying between two). Given that difficulty, my impression is that it's not really solvable, or at least not in a way that would result in a more efficient version.