Representing continuous probability distributions

Question

I have a problem involving a collection of continuous probability distribution functions, most of which are determined empirically (e.g. departure times, transit times). What I

Answer 1

I think the histograms or the list of 1/N area regions is a good idea. For the sake of argument, I'll assume that you'll have a fixed N for all distributions.

Use the paper you linked edit 4 to generate the new distribution. Then, approximate it with a new N-element distribution.

If you don't want N to be fixed, it's even easier. Take each convex polygon (trapezoid or triangle) in the new generated distribution and approximate it with a uniform distribution.