On binomial and circular binomial distributions of order \(k\) for \(l\)-overlapping success runs of length \(k\)

DOI10.1007/BF02762842zbMath1086.60010WikidataQ56010510 ScholiaQ56010510MaRDI QIDQ816557

Frosso S. Makri, Andreas N. Philippou

Publication date: 9 March 2006

Published in: Statistical Papers (Search for Journal in Brave)

zbMATH Keywords

recurrence relationsoccupancy problem

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Combinatorial probability (60C05)

Related Items (19)

Weak runs in sequences of binary trials ⋮ On monotonicity of expected values of some run-related distributions ⋮ On ℓ-overlapping Runs of Ones of Lengthkin Sequences of Independent Binary Random Variables ⋮ Stochastic ordering among success runs statistics in a sequence of exchangeable binary trials ⋮ Applications of Fuss-Catalan numbers to success runs of Bernoulli trials ⋮ Markov binomial distribution of order \(k\) and its applications ⋮ Computing waiting time probabilities related to \((k_1, k_2, \dots, k_l)\) pattern ⋮ Joint distributions of numbers of runs of specified lengths on directed trees ⋮ On runs of length exceeding a threshold: normal approximation ⋮ Run statistics in a sequence of arbitrarily dependent binary trials ⋮ Distributions of patterns of two successes separated by a string of \(k-2\) failures ⋮ On the joint distribution of success runs of several lengths in the sequence of MBT and its applications ⋮ On Occurrences of F-S Strings in Linearly and Circularly Ordered Binary Sequences ⋮ Generalizations of runs and patterns distributions for sequences of binary trials ⋮ Start-up demonstration tests with three-level classification ⋮ A Note on Circular m-consecutive-k-out-of-n:F Systems ⋮ \(g\)-geometric and \(g\)-binomial distributions of order image ⋮ Run Statistics Defined on the Multicolor URN Model ⋮ Polya, Inverse Polya, and Circular Polya Distributions of Orderkforl-Overlapping Success Runs

Cites Work

• On Ling's binomial and negative binomial distributions of order k
• Specific formulae for some success run distributions
• On binomial distributions of order k
• On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials
• Generalized binomial and negative binomial distributions of order \(k\) by the \(\ell\)-overlapping enumeration scheme
• Waiting Times and Number of Appearances of Runs: A Unified Approach
• A unified approach to binomial-type distributions of order k
• Runs on a circle
• Compound Poisson approximations for word patterns under Markovian hypotheses
• m-consecutive-k-out-of-n:F systems
• Successes, runs and longest runs
• Numbers of success-runs of specified length until certain stopping time rules and generalized binomial distributions of order \(k\)
• Distributions of numbers of success runs of fixed length in Markov dependent trials
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