Abstract
In the present article we investigate the exact distribution of the waiting time for the r-th non-overlapping appearance of a pair of successes separated by at mosk k−2 failures (k≥2) in a sequence of independent and identically distributed (iid) Bernoulli trials. Formulae are provided for the probability distribution function, probability generating function and moments and some asymptotic results are discussed. Expressions in terms of certain generalised Fibonacci numbers and polynomials are also included.
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Koutras, M.V. On a waiting time distribution in a sequence of Bernoulli trials. Ann Inst Stat Math 48, 789–806 (1996). https://doi.org/10.1007/BF00052333
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DOI: https://doi.org/10.1007/BF00052333