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Bivariate Markov chain embeddable variables of polynomial type

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Abstract

The primary aim of the present article is to provide a general framework for investigating the joint distribution of run length accumulating/enumerating variables by the aid of a Markov chain embedding technique. To achieve that we introduce first a class of bivariate discrete random variables whose joint distribution can be described by the aid of a Markov chain and develop formulae for their joint probability mass function, generating functions and moments. The results are then exploited for the derivation of the distribution of a bivariate run-related statistic. Finally, some interesting uses of our results in reliability theory and educational psychology are highlighted.

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Authors and Affiliations

  1. Department of Statistics and Insurance Science, University of Piraeus, Karaoli & Dimitriou 80, Piraeus, 18534, Greece

    M. V. Koutras, S. Bersimis & D. L. Antzoulakos

Authors
  1. M. V. Koutras
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  2. S. Bersimis
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  3. D. L. Antzoulakos
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Corresponding author

Correspondence to M. V. Koutras.

Additional information

Research supported by General Secretary of Research and Technology of Greece under grand PENED 2001.

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Koutras, M.V., Bersimis, S. & Antzoulakos, D.L. Bivariate Markov chain embeddable variables of polynomial type. AISM 60, 173–191 (2008). https://doi.org/10.1007/s10463-006-0080-6

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  • DOI: https://doi.org/10.1007/s10463-006-0080-6

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