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Multimodality of the Markov Binomial Distribution

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Michel Dekking  and
Derong Kong
Michel Dekking*
Affiliation:
Delft University of Technology
Derong Kong*
Affiliation:
Delft University of Technology
*
∗ Postal address: Delft University of Technology, Faculty EWI, PO Box 5031, 2600 GA Delft, The Netherlands.
∗ Postal address: Delft University of Technology, Faculty EWI, PO Box 5031, 2600 GA Delft, The Netherlands.
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Abstract

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We study the shape of the probability mass function of the Markov binomial distribution, and give necessary and sufficient conditions for the probability mass function to be unimodal, bimodal, or trimodal. These are useful to analyze the double-peaking results of a reactive transport model from the engineering literature. Moreover, we give a closed-form expression for the variance of the Markov binomial distribution, and expressions for the mean and the variance conditioned on the state at time n.

Keywords

Markov binomial distributionlog-concavitydouble peaking in kinetic transport

MSC classification

Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 48 , Issue 4 , December 2011 , pp. 938 - 953
Copyright
Copyright © Applied Probability Trust 2011 

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