Phase-type distributions and the structure of finite Markov chains

AbstractMaier, R.S., Phase-type distributions and the structure of finite Markov chains, Journal of Computational and Applied Mathematics 46 (1993) 449–453.We show that all discrete phase-type distributions arise as first passage times (i.e., absorption times) in finite-state Markov chains with a certain recursive internal structure. This arises from the special properties of an automata-theoretic algorithm which can be used to solve the inverse problem for phase-type distributions: the construction of a Markov chain with specified absorption time distribution