Characterization
The distribution of time X until the process reaches the absorbing state is said to be phase-type distributed and is denoted PH(α,S).
The distribution function of X is given by,
and the density function,
for all x > 0, where exp( · ) is the matrix exponential. It is usually assumed the probability of process starting in the absorbing state is zero (i.e. α0= 0). The moments of the distribution function are given by
Read more about this topic: Phase-type Distribution