On waiting time distribution of runs of ones or zeros in a Bernoulli sequence

Sungsu Kim, Chongjin Park and Jungtaek Oh

Statistics & Probability Letters, 2013, vol. 83, issue 1, 339-344

Abstract: Consider an infinite sequence of Bernoulli trials {Xi|i=1,2,…}. Let W(k) denote the waiting time, the number of trials needed, to get either consecutive k ones or k zeros for the first time. The probability distribution of W(k) is derived for both independent and homogeneous two-state Markovian Bernoulli trials, using a generalized Fibonacci sequence of order k. For independent Bernoulli trials, a special case of symmetric trial with p=12 is considered.

Keywords: Bernoulli sequences; Fibonacci sequences; Probability distribution function; Probability generating function; Sooner waiting time (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spl.2012.10.001

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