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https://hdl.handle.net/2440/37739
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DC Field | Value | Language |
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dc.contributor.advisor | Taylor, Peter | en |
dc.contributor.advisor | Bean, Nigel Geoffrey | en |
dc.contributor.author | Fackrell, Mark William | en |
dc.date.issued | 2003 | en |
dc.identifier.uri | http://hdl.handle.net/2440/37739 | - |
dc.description.abstract | A random variable that is defined as the absorption time of an evanescent finite-state continuous-time Markov chain is said to have a phase-type distribution. A phase-type distribution is said to have a representation (α,T ) where α is the initial state probability distribution and T is the infinitesimal generator of the Markov chain. The distribution function of a phase-type distribution can be expressed in terms of this representation. The wider class of matrix-exponential distributions have distribution functions of the same form as phase-type distributions, but their representations do not need to have a simple probabilistic interpretation. This class can be equivalently defined as the class of all distributions that have rational Laplace-Stieltjes transform. There exists a one-to-one correspondence between the Laplace-Stieltjes transform of a matrix- exponential distribution and a representation (β,S) for it where S is a companion matrix. In order to use matrix-exponential distributions to fit data or approximate probability distributions the following question needs to be answered: “Given a rational Laplace-Stieltjes transform, or a pair (β,S) where S is a companion matrix, when do they correspond to a matrix-exponential distribution?” In this thesis we address this problem and demonstrate how its solution can be applied to the abovementioned fitting or approximation problem. | en |
dc.format.extent | 1040629 bytes | en |
dc.format.extent | 136707 bytes | en |
dc.format.mimetype | application/pdf | en |
dc.format.mimetype | application/pdf | en |
dc.language.iso | en | en |
dc.subject | Markov processes, combinatorial set theory, algorithms | en |
dc.title | Characterization of matrix-exponential distributions. | en |
dc.type | Thesis | en |
dc.contributor.school | School of Applied Mathematics | en |
dc.provenance | This electronic version is made publicly available by the University of Adelaide in accordance with its open access policy for student theses. Copyright in this thesis remains with the author. This thesis may incorporate third party material which has been used by the author pursuant to Fair Dealing exception. If you are the author of this thesis and do not wish it to be made publicly available or If you are the owner of any included third party copyright material you wish to be removed from this electronic version, please complete the take down form located at: http://www.adelaide.edu.au/legals | - |
dc.description.dissertation | Thesis (Ph.D.)--School of Applied Mathematics, 2003. | en |
Appears in Collections: | Research Theses |
Files in This Item:
File | Description | Size | Format | |
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01front.pdf | 133.5 kB | Adobe PDF | View/Open | |
02whole.pdf | 933.65 kB | Adobe PDF | View/Open |
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