Definition
Consider a continuous-time Markov process with m+1 states, where m ≥ 1, such that the states 1,...,m are transient states and state 0 is an absorbing state. Further, let the process have an initial probability of starting in any of the m+1 phases given by the probability vector (α0,α) where α0 is a scalar and α is a 1×m vector.
The continuous phase-type distribution is the distribution of time from the above process's starting until absorption in the absorbing state.
This process can be written in the form of a transition rate matrix,
where S is an m×m matrix and S0 = -S1. Here 1 represents an m×1 vector with every element being 1.
Read more about this topic: Phase-type Distribution
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