Convolution of Binomial and Negative Binomial Variables |
| |
| Authors: | Tomoaki Imoto |
| |
| Institution: | 1. School of Fundamental Science and Technology, Keio University, Yokohama, Japaneureka-00.wakatta@a5.keio.jp |
| |
| 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. |
| |
| Keywords: | Birth death and immigration process Index of dispersion Kemp’s convolution of pseudo variables Random walk Thinned stochastic process |
|
|
