Special Cases
Just as the continuous time distribution is a generalisation of the exponential distribution, the discrete time distribution is a generalisation of the geometric distribution, for example:
- Degenerate distribution, point mass at zero or the empty phase-type distribution - 0 phases.
- Geometric distribution - 1 phase.
- Negative binomial distribution - 2 or more identical phases in sequence.
- Mixed Geometric distribution- 2 or more non-identical phases, that each have a probability of occurring in a mutually exclusive, or parallel, manner. This is the discrete analogue of the Hyperexponential distribution, but it is not called the Hypergeometric distribution, since that name is in use for an entirely different type of discrete distribution.
Read more about this topic: Discrete Phase-type Distribution
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