Definition
A terminating Markov chain is a Markov chain where all states are transient, except one which is absorbing. Reordering the states, the transition probability matrix of a terminating Markov chain with transient states is
where is a matrix and . The transition matrix is characterized entirely by its upper-left block .
Definition. A distribution on is a discrete phase-type distribution if it is the distribution of the first passage time to the absorbing state of a terminating Markov chain with finitely many states.
Read more about this topic: Discrete Phase-type Distribution
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