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A χ2 goodness-of-fit test for Markov renewal processesgoodness-of-fit test for Markov renewal processes

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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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Authors and Affiliations

  1. National Center for Health Statistics, Southern Methodist University, USA

    Dwight B. Brock & A. M. Kshirsagar

Authors
  1. Dwight B. Brock
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  2. A. M. Kshirsagar
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Additional information

Dwight B. Brock is mathematical statistican, Office of Statistical Methods, National Center for Health Statistics, Rockville, Maryland. A. M. Kshisagar is Associate Professor, Department of Statistics, Southern Methodist University. This research was partially supported by Office of Naval Research Contract No. N000 14-68-A-0515, and by NIH Training Grant GM-951, both with Southern Methodist University. This article is partially based on Dwight B. Brock's Ph.D. dissertation accepted by Southern Methodist University.

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Brock, D.B., Kshirsagar, A.M. A χ2 goodness-of-fit test for Markov renewal processesgoodness-of-fit test for Markov renewal processes. Ann Inst Stat Math 25, 643–654 (1973). https://doi.org/10.1007/BF02479406

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  • DOI: https://doi.org/10.1007/BF02479406

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