Accession Number : AD0725565

Title :   Statistical Inference for Markov Renewal Processes.

Descriptive Note : Technical rept.,

Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

Personal Author(s) : Brock,Dwight B.

Report Date : 15 APR 1971

Pagination or Media Count : 68

Abstract : 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)

Descriptors :   (*STOCHASTIC PROCESSES, MATHEMATICAL PREDICTION), (*STATISTICAL PROCESSES, STATISTICAL TESTS), SET THEORY, DISTRIBUTION FUNCTIONS, MATRICES(MATHEMATICS), RANDOM VARIABLES, ASYMPTOTIC SERIES, PARTIAL DIFFERENTIAL EQUATIONS

Subject Categories : Statistics and Probability
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE