Convergence rate for the longest T-contaminated runs of heads. Paper with detailed proofs

2023/02/13 by Fazekas, István, Fazekas, Borbála, Suja, Michael Ochieng
#60C05 60F05 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2302.06657

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 prove that the rate of the approximation of our accompanying distribution for the length of the longest T-contaminated head run is considerably better than the previous ones. For the proof we use a powerful lemma by Csáki, Földes and Komlós.

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