Title 
On the relation between matrixgeometric and discrete phasetype distributions 
Author

Greeuw, Sietske

Supervisor

Nielsen, Bo Friis (Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK2800 Kgs. Lyngby, Denmark)

Institution 
Technical University of Denmark, DTU, DK2800 Kgs. Lyngby, Denmark 
Thesis level 
Master's thesis 
Year 
2009 
Abstract 
A discrete phasetype distribution describes the time until absorption in a
discretetime Markov chain with a finite number of transient states and one
absorbing state. The density f(n) of a discrete phasetype 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 Markovchain interpretation, we obtain the
density of a matrixgeometric distribution. Matrixgeometric distributions can
equivalently be defined as distributions on the nonnegative integers that have
a rational probability generating function.
In this thesis it is shown that the class of matrixgeometric distributions is
strictly larger than the class of discrete phasetype distributions. We give an
example of a set of matrixgeometric distributions that are not of discrete phasetype.
We also show that there is a possible order reduction when representing
a discrete phasetype distribution as a matrixgeometric distribution.
The results parallel the continuous case, where the class of matrixexponential
distributions is strictly larger than the class of continuous phasetype distributions,
and where there is also a possible order reduction. 
Series 
IMMM.Sc.200937 
Admin 
Creation date: 20090624
Update date: 20100825
Source: dtu
ID: 245331
Original MXD
