On the relation between matrix-geometric and discrete phase-type distributions | Sietske Greeuw
| | Abstract | A discrete phase-type distribution describes the time until absorption in a discrete-time Markov chain with a finite number of transient states and one absorbing state. The density f(n) of a discrete phase-type distribution can be expressed by the initial probability vector T, the transition probability matrix T of the transient states of the Markov chain and the vector t containing the probabilities of entering the absorbing state from the transient states: f(n) = aTn1t, nEN.
If we take a probability density of the same form, but not necessarily require a, T and t to have the probabilistic Markov-chain interpretation, we obtain the density of a matrix-geometric distribution. Matrix-geometric distributions can equivalently be defined as distributions on the non-negative integers that have a rational probability generating function.
In this thesis it is shown that the class of matrix-geometric distributions is strictly larger than the class of discrete phase-type distributions. We give an example of a set of matrix-geometric distributions that are not of discrete phasetype. We also show that there is a possible order reduction when representing a discrete phase-type distribution as a matrix-geometric distribution.
The results parallel the continuous case, where the class of matrix-exponential distributions is strictly larger than the class of continuous phase-type distributions, and where there is also a possible order reduction. | | Type | Master's thesis [Academic thesis] | | Year | 2009 | | Publisher | Technical University of Denmark, Department of Applied Mathematics and Computer Science | | Address | Richard Petersens Plads, Building 324, DK-2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk | | Series | DTU Compute M.Sc.-2009 | | Note | Supervisor: Bo Friis Nielsen, bfni@dtu.dk | | Electronic version(s) | [pdf] | | Publication link | http://www.compute.dtu.dk/English.aspx | | BibTeX data | [bibtex] | | IMM Group(s) | Mathematical Statistics |
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