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- W1489279489 abstract "Flowgraph models are directed graph models for describing the dynamic changes in a stochastic process. They are one class of multistate models that are applied to analyse time-to-event data. The mainmotivation of the flowgraph models is to determine the distribution ofthe total waiting times until an event of interest occurs in a stochasticprocess that progresses through various states. This thesis applies themethodology of flowgraph models to the study of Markov and SemiMarkov processes.The underlying approach of the thesis is that the access to the moment generating function (MGF) and cumulant generating function(CGF), provided by Mason’s rule enables us to use the Method ofMoments (MM) which depends on moments and cumulant. We givea new derivation of the Mason’s rule to compute the total waitingMGF based on the internode transition matrix of a flowgraph. Next,we demonstrate methods to determine and approximate the distribution of total waiting time based on the inversion of the MGF, includingan alternative approach using the Pad´e approximation of the MGF,which always yields a closed form density.For parameter estimation, we extend the Expectation-Maximization(EM) algorithm to estimate parameters in the mixture of negativeweight exponential density. Our second contribution is to develop abias correction method in the Method of Moments (BCMM). By investigating methods for tail area approximation, we propose a newway to estimate the total waiting time density function and survival" @default.
- W1489279489 created "2016-06-24" @default.
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- W1489279489 date "2011-12-08" @default.
- W1489279489 modified "2023-09-23" @default.
- W1489279489 title "The methodology of flowgraph models" @default.
- W1489279489 hasPublicationYear "2011" @default.
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