SOME RESULTS ON r-TRUNCATED DEGENERATE POISSON RANDOM VARIABLES.

The zero-truncated Poisson distributions are certain discrete probability distributions whose supports are the set of positive integers, which are also known as the conditional Poisson distributions or the positive Poisson distributions. Recently, as a natural extension of those distributions, Kim–Kim studied the zero-truncated degenerate Poisson distributions. In this paper, we introduce the r -truncated degenerate Poisson random variable with parameter α > 0 , whose probability mass function is given by p λ , r (i) = (1) i , λ e λ (α) − e λ , r (α) α i i ! , (i = r + 1 , r + 2 , r + 3 , ...) , and investigate various properties of this random variable. [ABSTRACT FROM AUTHOR]