Phase-type Probability Distributions
The probability distributions of phase-type, or PH-distributions, form a useful general class for the representation of nonnegative random variables. A comprehensive discussion of their basic properties is given in Neuts (1981). There are parallel definitions and properties of discrete and continuous PH-distributions, but the discussion here emphasizes the continuous case.
The simplest example is the Erlang random variable, which can be expressed as the sum of independent exponentially distributed random variables. As a result, one can construct a realization of an Erlang random variable by going through a series of phases, one for each exponential random variable; hence, the Erlang distribution is a phase-type distribution. Generalizing this phase-type idea governs the movement through the phases by a Markov chain that permits movement back and forth between the interior phases, with the final stage being an absorbing barrier.
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