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... moreI 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 need is some way of taking two of these PDFs and doing arithmetic on them. E.g. if I have two values x taken from PDF X, and y taken from PDF Y, I need to get the PDF for (x+y), or any other operation f(x,y).
An analytical solution is not possible, so what I'm looking for is some representation of PDFs that allows such things. An obvious (but computationally expensive) solution is monte-carlo: generate lots of values of x and y, and then just measure f(x, y). But that takes too much CPU time.
I did think about representing the PDF as a list of ranges where each range has a roughly equal probability, effectively representing the PDF as the union of a list of uniform distributions. But I can't see how to combine them.
Does anyone have any good solutions to this problem?
Edit: The goal is to create a mini-language (aka Domain... less