Status: fitting monotonic splines to t-digest cdf sketches.
Plots by EvilPlot
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Got it, I had misinterpreted the green bins (on both plots) as the t-digest output, but of course in retrospect the even bin widths wouldn't make sense for that.
I've been working up an idea for explaining t-digests as a histogram where the bin locations (and implied widths) are individually updated, and where new bins can be added. Conversely, a t-digest where the clusters are fixed and evenly spaced is a histogram.
I assume a t-digest ends up being basically an equal-area (vs equal-width) histogram?
It's not even equal-area. There are upper bounds on cluster mass, but not any lower bound. A newly-added cluster may be quite small. Clusters move around as data land on them, so there is no particular regularity. That's how the sketch moves in response to data.
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