I tried to guess the meaning of the curves in your medium article, and I failed with all. Either I am more stupid than I know or the graphs need to be augmented with word descriptions to help the interpretation. If its the latter, why need graphs?
If this is just about capturing duration, won't an annotated bar be better than a curve of arbitrary slope and shape?
Small nit: if the curve is continuous, should the y-axis be labeled density rather than probability? Closely linked: is anything being done to ensure the curve integrates to 1? I imagine the answer is "the scale changes as you draw", but that seems a bit confusing since drawing doesn't usually change the structure of the surface being drawn on.
Given the target use case for this, isn't that a bit of misplaced precision? Unless your boss is a quant, then the distinction will likely just go over their head, or worse, interfere with the gist of the message trying to be conveyed.
biggest problem I see is that it projects a misleading vaneer of precision. Others might take it too literally. Suggestion: use cartoon-like graphs/fonts to convey idea that these are back of the envelope projections.
