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On runs of length exceeding a threshold: normal approximation

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Abstract

Run statistics denoting number of runs and sum of run lengths are defined on binary sequences and their asymptotic normality is established by a simple unified way for Bernoulli sequences. All the considered statistics share a common feature; they refer to runs of length exceeding a specific length (a threshold). Asymptotic results of associated statistics denoting run lengths and waiting times are derived as well. Specific probabilities of the examined statistics are used in applications in the fields of system reliability and molecular biology. The study is illustrated by an extensive numerical experimentation.

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Authors and Affiliations

  1. Department of Mathematics, University of Patras, 26500, Patras, Greece

    Frosso S. Makri

  2. Department of Physics, University of Patras, 26500, Patras, Greece

    Zaharias M. Psillakis

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  1. Frosso S. Makri
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  2. Zaharias M. Psillakis
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Correspondence to Frosso S. Makri.

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Makri, F.S., Psillakis, Z.M. On runs of length exceeding a threshold: normal approximation. Stat Papers 52, 531–551 (2011). https://doi.org/10.1007/s00362-009-0268-y

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