Generalized binomial and negative binomial distributions of order \(k\) by the \(\ell\)-overlapping enumeration scheme

zbMath1057.62011MaRDI QIDQ1881384

Sigeo Aki, Kiyoshi Inoue

Publication date: 5 October 2004

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

zbMATH Keywords

probability generating functionPoisson distributionnegative binomial distributiondouble generating function\(\ell\)-overlapping enumeration scheme\(\ell\)-overlapping occurrence of success-runsdistribution of the waiting timeMarkov chain embedding methodtwo-state Markov dependent trials

Mathematics Subject Classification ID

Exact distribution theory in statistics (62E15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Combinatorial probability (60C05) Reliability and life testing (62N05) Applications of Markov renewal processes (reliability, queueing networks, etc.) (60K20)

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Joint distributions associated with patterns, successes and failures in a sequence of multi-state trials ⋮ Weak runs in sequences of binary trials ⋮ Joint distributions of runs in a sequence of higher-order two-state Markov trials ⋮ Applications of Fuss-Catalan numbers to success runs of Bernoulli trials ⋮ On the modes of the negative binomial distribution of order k, type I ⋮ Bivariate Fibonacci polynomials of order \(k\) with statistical applications ⋮ Joint distributions of numbers of runs of specified lengths on directed trees ⋮ Distributions of patterns of two successes separated by a string of \(k-2\) failures ⋮ A compound negative binomial distribution with mutative termination conditions based on a change point ⋮ On the joint distribution of success runs of several lengths in the sequence of MBT and its applications ⋮ Joint distributions of numbers of runs of specified lengths in a sequence of Markov dependent multistate trials ⋮ Generalizations of runs and patterns distributions for sequences of binary trials ⋮ On the conditional and unconditional distributions of the number of success runs on a circle with applications ⋮ On Generating Functions of Waiting Times and Numbers of Occurrences of Compound Patterns in a Sequence of Multistate Trials ⋮ Joint distributions of numbers of success runs of specified lengths in linear and circular se\-quences ⋮ On binomial and circular binomial distributions of order \(k\) for \(l\)-overlapping success runs of length \(k\) ⋮ A generalized Pólya urn model and related multivariate distributions

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