Distributions related to \((k_{1},k_{2})\) events

DOI10.1016/j.jspi.2009.12.019zbMath1195.60024OpenAlexW196017415WikidataQ56010506 ScholiaQ56010506MaRDI QIDQ963855

Demetrios L. Antzoulakos, Spiros D. Dafnis, Andreas N. Philippou

Publication date: 14 April 2010

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2009.12.019

zbMATH Keywords

momentswaiting timesuccess runsbinomialrecursiveconsecutivePólya-Eggenberger

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Probability distributions: general theory (60E05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10)

Related Items (15)

Exact distributions of constrained \((k, \ell )\) strings of failures between subsequent successes ⋮ On discrete Gibbs measure approximation to runs ⋮ Multiple consecutive runs of multi-state trials: distributions of \(( k_1 , k_2 , \dots , k_\ell )\) patterns ⋮ Waiting time for consecutive repetitions of a pattern and related distributions ⋮ Computing waiting time probabilities related to \((k_1, k_2, \dots, k_l)\) pattern ⋮ Generalizations of distributions related to \((k_1,k_2)\)-runs ⋮ A compound Poisson convergence theorem for sums of \(m\)-dependent variables ⋮ Distributions of \((k_1,k_2,\dots ,k_m)\)-runs with multi-state trials ⋮ Distributions related to weak runs with a minimum and a maximum number of successes: a unified approach ⋮ Exact and asymptotic results for pattern waiting times ⋮ Distributions associated with \((k_1,k_2)\) events on semi-Markov binary trials ⋮ Distributions of patterns of two successes separated by a string of \(k-2\) failures ⋮ On distributions of runs in the compound binomial risk model ⋮ Counting certain binary strings ⋮ Pseudo-binomial approximation to \((k_1, k_2)\)-runs

Cites Work

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• Poisson approximation for (k₁, k₂)-events via the Stein-Chen method
• On discrete distributions of order k
• Successes, runs and longest runs
• Distributions of numbers of success runs of fixed length in Markov dependent trials

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