Abstract
Let us consider a random sample X 1, …, X n of size n drawn on a Bernoulli r.v. X taking the values 0 and 1 with probabilities p and q (p + q = 1) respectively. Let N n denote the number of non-overlapping runs in l’s of length (fixed) k ≥ 2, and M n , M c n the number of overlapping runs in l’s of length k in the linear and cyclic case respectively. Throughout the present paper, to avoid trivialities, n and k are given positive integers such that n ≥ k. To make clear the difference between N n , M n′ , M c n , we mention, by way of example, that for the sequence 1111001101110101 and k = 3 we have N 16 = 2, M 16 = 3 and M c16 = 4. By convention M o = M c0 = 0.
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© 1993 Springer Science+Business Media Dordrecht
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Chryssaphinou, O., Papastavridis, S., Tsapelas, T. (1993). On the Number of Overlapping Success Runs in a Sequence of Independent Bernoulli Trials. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2058-6_10
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DOI: https://doi.org/10.1007/978-94-011-2058-6_10
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