For many applications, detailed statistical models are overkill. Instead, we can get away with a rough description of the distribution – not in mathematical formula form, but just as a graph with a few sample points.
For example, when trying to model the traffic around a school, you might know that the graph looks something like this:
The input is the number of minutes before the first bell rings, and the output the number of children dropped off at that time. You know that most kids are brought before the bell rings, and that the closer to the bell, the more kids are being brought every minute. Only a few kids are late.
This tutorial describes how to generate random numbers that can generate a distribution described by an arbitrary (piece-wise linear) curve, as the one above.