# 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):

# Report Date:

## 1971-04-15

# Pagination or Media Count:

## 68.0

# 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:

# Subject Categories:

- Statistics and Probability
- Operations Research