Journal of Applied Probability

Multimodality of the Markov binomial distribution

Michel Dekking and Derong Kong

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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.

Article information

J. Appl. Probab., Volume 48, Number 4 (2011), 938-953.

First available in Project Euclid: 16 December 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60J20: Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]

Markov binomial distribution log-concavity double peaking in kinetic transport


Dekking, Michel; Kong, Derong. Multimodality of the Markov binomial distribution. J. Appl. Probab. 48 (2011), no. 4, 938--953. doi:10.1239/jap/1324046011.

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