Statistical Inference for Markov Renewal Processes

A Markov Renewal Process is one which records at each time t the number of times a system visits each of a finite number (m) of states up to time t. The system moves from state to state according to a Markov chain, and the time required for each move (sojourn time) is a random variable whose distrib...

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Bibliographic Details
Main Author: Brock,Dwight B
Format: Report
Language:English
Subjects:
ASYMPTOTIC SERIES
BAYESIAN ANALYSIS
CHI SQUARE TEST
DISTRIBUTION FUNCTIONS
MARKOV CHAINS
MARKOV RENEWAL PROCESSES
MATHEMATICAL PREDICTION
MATRICES(MATHEMATICS)
Operations Research
PARTIAL DIFFERENTIAL EQUATIONS
RANDOM VARIABLES
SET THEORY
STATISTICAL INFERENCE
STATISTICAL PROCESSES
STATISTICAL TESTS
Statistics and Probability
STOCHASTIC PROCESSES
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Summary:A Markov Renewal Process is one which records at each time t the number of times a system visits each of a finite number (m) of states up to time t. The system moves from state to state according to a Markov chain, and the time required for each move (sojourn time) is a random variable whose distribution function may depend on the two states between which the move is made. In this paper the author develops a test for the goodness of fit of a hypothetical transition probability matrix for a Markov Renewal Process. The author illustrates this procedure numerically by applying it to a realization of a two-state Markov Renewal Process artificially generated on a computer. In addition, the author considers some Bayesian analysis for Markov Renewal Processes by assuming a matrix beta prior distribution for the transition probability matrix. The report also discusses a special case of this topic and gives an illustration for a two-state Markov Renewal Process. In the final chapter a summary of results is given and some possible future research proglems are indicated. (Author)