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

A couple of responses:

1) If you have empirically determined PDFs they either you have histograms or you have an approximation to a parametric PDF. A PDF is a continuous function and you don't have infinite data...

2) Let's assume that the variables are independent. Then if you make the PDF discrete then P(f(x,y)) = f(x,y)p(x,y) = f(x,y)p(x)p(y) summed over all the combinations of x and y such that f(x,y) meets your target.

If you are going to fit the empirical PDFs to standard PDFs, e.g. the normal distribution, then you can use already-determined functions to figure out the sum, etc.

If the variables are not independent, then you have more trouble on your hands and I think you have to use copulas.

I think that defining your own mini-language, etc., is overkill. you can do this with arrays...