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Convergence rate for the longest T-contaminated runs of heads

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  • Fazekas, István
  • Fazekas, Borbála
  • Suja, Michael Ochieng

Abstract

We study the length of T-contaminated runs of heads in the well-known coin tossing experiment. A T-contaminated run of heads is a sequence of consecutive heads interrupted by T tails. For T=1 and T=2 we find the asymptotic distribution for the first hitting time of the T contaminated run of heads having length m; furthermore, we obtain a limit theorem for the length of the longest T-contaminated head run. We find the rate of the approximation of our accompanying distribution for the length of the longest T-contaminated head run. For the proof we use a powerful lemma of Csáki et al. (1987).

Suggested Citation

  • Fazekas, István & Fazekas, Borbála & Suja, Michael Ochieng, 2024. "Convergence rate for the longest T-contaminated runs of heads," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715224000282
    DOI: 10.1016/j.spl.2024.110059
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    References listed on IDEAS

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    1. Novak, S.Y., 2017. "On the length of the longest head run," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 111-114.
    2. Binswanger, K. & Embrechts, P., 1994. "Longest runs in coin tossing," Insurance: Mathematics and Economics, Elsevier, vol. 15(2-3), pages 139-149, December.
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