On the two-parameter Bell-Touchard discrete distribution

摘要

In this paper we introduce a new two-parameter discrete distribution which may be useful for modeling count data. Additionally, the probability mass function is very simple and it may have a zero vertex. We show that the new discrete distribution is a particular solution of a multiple Poisson process, and that it is infinitely divisible. Additionally, various structural properties of the new discrete distribution are derived. We also discuss two methods (moments and maximum likelihood) to estimate the model parameters. The usefulness of the proposed distribution is illustrated by means of real data sets to prove its versatility in practical applications.