Abstract
Maier, 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.
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