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On the Distribution of the Number of Success Runs in a Continuous Time Markov Chain

Boutsikas V. Michael () and Vaggelatou Eutichia ()
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Boutsikas V. Michael: University of Piraeus
Vaggelatou Eutichia: National and Kapodistrian University of Athens

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 3, 969-993

Abstract: Abstract We propose a continuous-time adaptation of the well-known concept of success runs by considering a marked point process with two types of marks (success-failure) that appear according to an appropriate continuous-time Markov chain. By constructing a bivariate imbedded process (consisting of a run-counting and a phase process), we offer recursive formulas and generating functions for the distribution of the number of runs and the waiting time until the appearance of the n-th success run. We investigate the three most popular counting schemes: (i) overlapping runs of length k, (ii) non-overlapping runs of length k and (iii) runs of length at least k. We also present examples of applications regarding: the total penalty cost in a maintenance reliability system, the number of risky situations in a non-life insurance portfolio and the number of runs of increasing (or decreasing) asset price movements in high-frequency financial data.

Keywords: Run statistics; Marked point process; Continuous-time Markov chain; Waiting time; Exact distribution; Markov chain imbedding technique; Generating function; Laplace transform; Primary 60J28; 60E10; Secondary: 62E15; 60G40 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-019-09743-3

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