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Convolution of Binomial and Negative Binomial Variables

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  • Tomoaki Imoto

Abstract

This paper considers a distribution formed by convolution of binomial and negative binomial variables. The distribution has the flexibility to adapt to the model under, equi, and over dispersion. Some properties of the proposed distribution are discussed, including characterization. Three stochastic processes leading to the distribution are also considered: (1) a three-dimensional random walk; (2) a birth, death, and immigration process; and (3) a thinned stochastic process.

Suggested Citation

  • Tomoaki Imoto, 2015. "Convolution of Binomial and Negative Binomial Variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(23), pages 5005-5022, December.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:23:p:5005-5022
    DOI: 10.1080/03610926.2013.809110
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