On success runs of length exceeded a threshold

DOI10.1007/s11009-009-9147-1zbMath1230.60012OpenAlexW2080680177MaRDI QIDQ539513

Zaharias M. Psillakis, Frosso S. Makri

Publication date: 30 May 2011

Published in: Methodology and Computing in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11009-009-9147-1

zbMATH Keywords

waiting timeMarkov chainBernoulli trialssuccess runsexceedancesexchangeable trialslinear and circular binary sequenceslongest run lengthPoisson trialsPolya-Eggenberger sampling schemereliability of consecutive systems

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Probability distributions: general theory (60E05) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Combinatorial probability (60C05)

Related Items (21)

On runs of ones defined on a \(q\)-sequence of binary trials ⋮ Runs in coin tossing: a general approach for deriving distributions for functionals ⋮ Weak runs in sequences of binary trials ⋮ On longest consecutive patterns in Markov chains ⋮ A family of induced distributions ⋮ Exact distributions of constrained \((k, \ell )\) strings of failures between subsequent successes ⋮ Stochastic ordering among success runs statistics in a sequence of exchangeable binary trials ⋮ Distributions of statistics describing concentration of runs in non homogeneous Markov-dependent trials ⋮ Analysis of joint reliability importance in linear m-consecutive-k,l -out-of-n:F system ⋮ Markov binomial distribution of order \(k\) and its applications ⋮ Joint distribution of run statistics in partially exchangeable processes ⋮ On success runs in a sequence of dependent trials with a change point ⋮ Discrete time shock models involving runs ⋮ Distributions related to weak runs with a minimum and a maximum number of successes: a unified approach ⋮ On distributions of runs in the compound binomial risk model ⋮ On the distribution of the number of success runs in a continuous time Markov chain ⋮ Counting certain binary strings ⋮ On Occurrences of F-S Strings in Linearly and Circularly Ordered Binary Sequences ⋮ Generalizations of runs and patterns distributions for sequences of binary trials ⋮ On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials ⋮ Discrete Scan Statistics Generated by Exchangeable Binary Trials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Distribution theory of runs via exchangeable random variables
• A direct method to obtain the joint distribution of successes, failures and patterns in enumeration problems
• A generalized geometric distribution and some of its properties
• Simple expressions for success run distributions in Bernoulli trials
• Non-parametric randomness tests based on success runs of fixed length
• Modeling claim exceedances over thresholds.
• On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials
• The exact and limiting distributions for the number of successes in success runs within a sequence of Markov-dependent two-state trials
• On the distribution of the total number of run lengths
• Longest runs in coin tossing
• Useful inequalities for the longest run distribution
• Some results associated with the longest run statistic in a sequence of Markov dependent trials
• Shortest and longest length of success runs in binary sequences
• Success runs in a sequence of exchangeable binary trials
• On the normal approximation for the distribution of the number of simple or compound patterns in a random sequence of multi-state trials
• New improved bounds for reliability of consecutive-k-out-of-n:F systems
• On the Distribution of the Number of Exceedances
• Poisson approximation and dna sequence matching
• Exact Reliability Formulas for Linear & Circular Consecutive-k-out-of-n:F Systems
• Simplified Reliabilities for Consecutive-k-out-of-nSystems
• Reliability Determination of a r-Successive-out-of-n:F System
• On the Consecutive-k-of-n:F System
• An improved Bonferroni inequality and applications
• De Finetti's Theorem on Exchangeable Variables
• Distribution Theory of Runs: A Markov Chain Approach
• Lengths of runs and waiting time distributions by using Pólya-Eggenberger sampling scheme
• On exact and large deviation approximation for the distribution of the longest run in a sequence of two-state Markov dependent trials
• A Full Likelihood Procedure for Analysing Exchangable Binary Data
• GERT Analysis of m-consecutive-k-out-of-n:F Systems with Dependence
• Success run statistics defined on an urn model
• Probability and Computing
• The Distribution Theory of Runs
• Distributions of numbers of success runs of fixed length in Markov dependent trials

This page was built for publication: On success runs of length exceeded a threshold