Journal of Applied Probability

Multimodality of the Markov binomial distribution

Michel Dekking and Derong Kong

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Abstract

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

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

Dates
First available in Project Euclid: 16 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.jap/1324046011

Digital Object Identifier
doi:10.1239/jap/1324046011

Mathematical Reviews number (MathSciNet)
MR2896660

Zentralblatt MATH identifier
1231.60064

Subjects
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]

Keywords
Markov binomial distribution log-concavity double peaking in kinetic transport

Citation

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


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