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The Binomial and Negative Binomial Distribution in Discrete Time Markov Chains

  • The classical results of the binomial and negative binomial probability distribution are generalized by means of homogeneous Discrete Time Markov Chains to series of stochastically independent random trials. These have not only two possible outcomes but two groups of them -- different kinds of successes and failures with occurrence probabilities depending on the outcome of the previous trial. This generalization allows a uniform view of occupation time, first passage time and recurrence time. Our results are consequently derived and presented in matrix form, the probabilities as well as the moments. They can be applied to all Discrete Time Markov Chains, especially in computer capacity planning, performability and economics.

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Metadaten
Author:Ludwig Frank
Parent Title (English):Markov Processes And Related Fields
Document Type:Article (peer reviewed)
Language:English
Publication Year:2017
Tag:binomial distribution; discrete time Markov Chains; first passage time; matrix representation; occupation time; recurrence time
Volume:23
Issue:3
First Page:377
Last Page:400
Peer reviewed:Ja
faculties / departments:Fakultät für Informatik