Abstract
A Markov Renewal Process (M.R.P.) is a process similar to a Markov chain, except that the time required to move from one state to another is not fixed, but is a random variable whose distribution may depend on the two states between which the transition is made. For an M.R.P. ofm (<∞) states we derive a goodness-of-fit test for a hypothetical matrix of transition probabilities. This test is similar to the test Bartlett has derived for Markov chains. We calculate the first two moments of the test statistic and modify it to fit the moments of a standard χ2. Finally, we illustrate the above procedure numeerically for a particular case of a two-state M.R.P.
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