Bilateral phase type distributions

A new class of probability distributions called "bilateral phase type distributions (BPH)" on (-∞, ∞) is defined as a generalization of the versatile class of phase type (PH) distributions on [0, ∞) introduced by Marcel F. Neuts. We derive the basic descriptors of such distributions in an algorithmically tractable manner and show that this class has many interesting closure properties and is dense in the class of all distributions on the real line. Based on the established versatility and tractability of phase type distributions, we believe that this class has high potential for general use in statistics, particularly to cover non-normal distributions, and also that its inherent connection to Markov chains may make it suitable for inference based on hidden Markov chain methods and MCMC type approaches.