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
Famous quotes containing the words special and/or cases:
“For universal love is as special an aspect as carnal love or any of the other kinds: all forms of mental and spiritual activity must be practiced and encouraged equally if the whole affair is to prosper. There is no cutting corners where the life of the soul is concerned....”
—John Ashbery (b. 1927)
“And in cases where profound conviction has been wrought, the eloquent man is he who is no beautiful speaker, but who is inwardly drunk with a certain belief. It agitates and tears him, and perhaps almost bereaves him of the power of articulation.”
—Ralph Waldo Emerson (1803–1882)