A triptych on three continuous analogs of the Poisson, binomial, and negative binomial distributions

Abstract

The classical Poisson, binomial, and negative binomial are among the most well-known and widely used discrete probability models, used across many different areas of applications. We discuss very natural continuous analogs of these distributions and present basic facts related to these new models, which were partially discussed in the literature. New results and generalizations related to these distributions are presented as well, which shed light on their potential applications. In particular, we discuss computational issues connected with these models, which would arise in their practical implementation due to non-explicit nature of their basic characteristics.