Beta 1

Title On the relation between matrix-geometric and discrete phase-type distributions
Author Greeuw, Sietske
Supervisor Nielsen, Bo Friis (Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2009
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 , 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) = Tn−1t, n 2 N. If we take a probability density of the same form, but not necessarily require , 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.
Series IMM-M.Sc.-2009-37
Admin Creation date: 2009-06-24    Update date: 2010-08-25    Source: dtu    ID: 245331    Original MXD