Successes, runs and longest runs

DOI10.1016/0167-7152(86)90025-8zbMath0584.60024OpenAlexW1985866648WikidataQ56010523 ScholiaQ56010523MaRDI QIDQ5903000

Andreas N. Philippou, Frosso S. Makri

Publication date: 1986

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-7152(86)90025-8

zbMATH Keywords

binomial distributionBernoulli trialslength of the longest success runnumber of success runs of length k

Mathematics Subject Classification ID

Combinatorial probability (60C05) Distribution theory (60E99)

Related Items (19)

Exact probability of fixed patterns occurring in a random sequence ⋮ Some results associated with the longest run statistic in a sequence of Markov dependent trials ⋮ Runs in coin tossing: a general approach for deriving distributions for functionals ⋮ A unified approach to binomial-type distributions of order k ⋮ Weak runs in sequences of binary trials ⋮ On longest consecutive patterns in Markov chains ⋮ Binomial distribution of order \(k\) in a modified binary sequence ⋮ Sooner and later waiting time problems for success and failure runs in higher order Markov dependent trials ⋮ Consecutive dual failure mode shock systems ⋮ Exact and asymptotic results for pattern waiting times ⋮ Chess, chance and conspiracy ⋮ On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials ⋮ Waiting time distributions of runs in higher order Markov chains ⋮ A test statistic for weighted runs ⋮ Waiting Times and Number of Appearances of Runs: A Unified Approach ⋮ Run Statistics Defined on the Multicolor URN Model ⋮ Formulae and recursions for the joint distributions of success runs of several lengths in a two-state Markov chain ⋮ Distribution theory of runs via exchangeable random variables ⋮ On Ling's binomial and negative binomial distributions of order k

Cites Work

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• A generalized geometric distribution and some of its properties
• Properties of the extended distributions of order k
• The Negative Binomial Distribution of Orderk and Some of Its Properties
• Longest run of consecutive observations having a specified attribute
• On discrete distributions of order k

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