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What sort of distributions should be allowed for numerical questions?

It's pretty clear that the single-gaussian(ish) function is insufficient to cover the breadth of different distributions people would like to enter in numerical predictions. It is, however, quite nontrivial to work out exactly what there should be.

A current proposal on the table is that as a "power" (i.e. that you get at a certain level or buy with tachyons) you can get a second gaussian (or perhaps more), and that as another power, you can get a piecewise-linear function.

Subtleties:

  • For each additional function, there is another parameter that is its overall normalization

  • As for the current gaussian, we also need to retain a way to express how much of the PDF lies off the edges of the range.

  • There has to be a workable UI.

Thoughts on the sort of distributions you have wanted to be able to express but have not been able to? Would the above suffice to cover your needs or should we contemplate something different?