Simple expressions for success run distributions in Bernoulli trials

DOI10.1016/S0167-7152(96)00022-3zbMath0879.60012MaRDI QIDQ1359710

Marco Muselli

Publication date: 6 July 1997

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

zbMATH Keywords

Bernoulli trialslongest success rundiscrete distributions of order \(k\)number of success runs

Mathematics Subject Classification ID

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

Related Items (19)

Generalized waiting time distributions associated with runs ⋮ On the Combinatorics of Placing Balls into Ordered Bins ⋮ 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 ⋮ Success run waiting times and Fuss-Catalan numbers ⋮ Applications of Fuss-Catalan numbers to success runs of Bernoulli trials ⋮ Approximations for success run probabilities in Bernoulli trials ⋮ The distributions of sum, minima and maxima of generalized geometric random variables ⋮ Distributions related to weak runs with a minimum and a maximum number of successes: a unified approach ⋮ The distribution of extended discrete random sums and its application to waiting time distributions ⋮ Distributions of random variables involved in discrete censored δ-shock models ⋮ On the modes of the negative binomial distribution of order k ⋮ Shortest and longest length of success runs in binary sequences ⋮ Geometric distribution of order \(k\) with a reward ⋮ On success runs of length exceeded a threshold ⋮ On the distribution of runs of ones in binary strings ⋮ A test statistic for weighted runs ⋮ Success run statistics defined on an urn model

Cites Work

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• Specific formulae for some success run distributions
• A generalized geometric distribution and some of its properties
• Properties of the extended distributions of order k
• Exact Reliability Formulas for Linear & Circular Consecutive-k-out-of-n:F Systems
• Simplified Reliabilities for Consecutive-k-out-of-nSystems
• Longest run of consecutive observations having a specified attribute
• Successes, runs and longest runs

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