A construction and minimization service for continuous probability distributions

The universe of acyclic continuous-time Markov chains can provide arbitrarily close approximations of any continuous probability distribution. We span this universe by a compositional construction calculus for acyclic phase-type distributions. The calculus draws its expressiveness from a single operator, yet the calculus is equipped with further convenient operators, namely convolution, maximum, and minimum. However, the size of the chains constructed in this way can grow rapidly. We therefore link our calculus to a compositional minimization algorithm that whenever applied almost surely yields a chain with the least possible size. The entire approach is available in the form of an easy-to-use web service. The paper describes the architecture of this service in detail and reports on experimental evidence demonstrating its usefulness.