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

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.

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Year of publication:	2013
Authors:	Kim, Sungsu ; Park, Chongjin ; Oh, Jungtaek
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 83.2013, 1, p. 339-344
Publisher:	Elsevier
Subject:	Bernoulli sequences \| Fibonacci sequences \| Probability distribution function \| Probability generating function \| Sooner waiting time

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040050