Web UI for inputting a function from the reals to the reals, such as a probability distribution.

Question

I would like a web interface for a user to describe a one-dimensional real-valued function. I'm imagining the user being presented with a blank pair of axes and they can click anywhere to create points that are thick and draggable. Double-clicking a point, let's say, makes it disappear. The actual function should be shown in real time as an interpolation of the user-supplied points.

Here's what this looks like implemented in Mathematica (though of course I'm looking for something in javascript):

Answer 1

Remember that a probability distribution has to be monotonically non-decreasing over its entire run, which your example is not. Even worse, that small dip is not due to user error -- their points are increasing as required -- but is an artifact of the interpolation method. If you use linear interpolation, then any non-monotonicity is your user's fault, and you can warn them.

Answer 2

The Distribution Builder tool by Dan Goldstein has an alternative interface for eliciting probability distributions.