Degenerate Zero-Truncated Poisson Random Variables

Recently, the degenerate Poisson random variable with parameter α > 0 , whose probability mass function is given by Pλ(i) = eλ⁻¹ (α) αⁱi! (1)i,λ (i = 0,1,2,) , was studied. In probability theory, the zero-truncated Poisson distributions are certain discrete probability distributions whose supports are the set of positive integers. These distributions are also known as the conditional Poisson distributions or the positive Poisson distributions. In this paper, we introduce the degenerate zero-truncated Poisson random variables whose probability mass functions are a natural extension of the zero-truncated Poisson distributions, and investigate various properties of those random variables.