Zero-Truncated Bell Distribution

Abstract

In this paper, the zero-truncated Bell distribution is introduced. It is modified from Bell distribution. Its probability mass function is derived. Some properties of the distribution are presented, e.g., mean and variance. Maximum likelihood estimation is employed for model parameter estimation. Finally, the proposed distribution is applied to fit with a real data set. The finding result of fitting the proposed distribution to real data set is included. It shows that the proposed distribution has the smallest minus log-likelihood where fitting to the real data set among zero-truncated Poisson and zero-truncated Poisson-Shanker distributions.