Distributions of numbers of failures and successes until the first consecutive \(k\) successes

DOI10.1007/BF00773603zbMath0806.60006MaRDI QIDQ1336554

Sigeo Aki, Katuomi Hirano

Publication date: 14 February 1995

Published in: Annals of the Institute of Statistical Mathematics (Search for Journal in Brave)

zbMATH Keywords

waiting timeMarkov chaingeometric distributioninverse sampling

Mathematics Subject Classification ID

Probability distributions: general theory (60E05) Applications of renewal theory (reliability, demand theory, etc.) (60K10)

Related Items (16)

Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials ⋮ Joint distributions of runs in a sequence of higher-order two-state Markov trials ⋮ Joint distributions of numbers of success-runs and failures until the first consecutive \(k\) successes ⋮ MULTIVARIATE GENERALIZED POLYA DISTRIBUTION OF ORDERk ⋮ Explicit distributional results in pattern formation ⋮ A direct method to obtain the joint distribution of successes, failures and patterns in enumeration problems ⋮ Bivariate Fibonacci polynomials of order \(k\) with statistical applications ⋮ The distribution of the length of the longest increasing subsequence in random permutations of arbitrary multi-sets ⋮ On the modes of the negative binomial distribution of order k ⋮ On the waiting time for the first success run ⋮ On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials ⋮ On occurrence of subpattern and method of gambling teams ⋮ Waiting Times and Number of Appearances of Runs: A Unified Approach ⋮ Run and Frequency Quotas Under Markovian Fashion and their Application in Risk Analysis ⋮ Discrete distributions related to success runs of lengthk in aulti-state markov chain ⋮ An algorithm to compute the probability of a run in binary fourth-order Markovian trials.

Cites Work

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• Sooner and later waiting time problems for Bernoulli trials: Frequency and run quotas
• A generalized geometric distribution and some of its properties
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• On binomial distributions of order k
• Quota sampling for multinomial via Dirichlet
• Waiting time problems for a sequence of discrete random variables
• On multiparameter distributions of order k
• On discrete distributions of order k
• On discrete distributions of order k

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