Bivariate Fibonacci polynomials of order \(k\) with statistical applications

DOI10.1007/s10463-008-0217-xzbMath1435.11035OpenAlexW2106258389MaRDI QIDQ907093

Kiyoshi Inoue, Sigeo Aki

Publication date: 1 February 2016

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

Full work available at URL: https://doi.org/10.1007/s10463-008-0217-x

zbMATH Keywords

probability generating functionwaiting timecontinued fractionsuccess runsFibonacci polynomialsdistributions of order \(k\)Lucas polynomials

Mathematics Subject Classification ID

Characteristic functions; other transforms (60E10) Exact enumeration problems, generating functions (05A15) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Continued fractions (11A55) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

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Cites Work

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• Joint distributions of numbers of success runs of specified lengths in linear and circular se\-quences
• Distributions of numbers of failures and successes until the first consecutive \(k\) successes
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• Runs, scans and urn model distributions: A unified Markov chain approach
• Joint distributions of numbers of runs of specified lengths in a sequence of Markov dependent multistate trials
• On the waiting time for the first success run
• On a class of polynomials related to classical orthogonal and Fibonacci polynomials with probability applications
• Distribution Theory of Runs: A Markov Chain Approach
• Runs on a circle
• On Generating Functions of Waiting Times and Numbers of Occurrences of Compound Patterns in a Sequence of Multistate Trials
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