On the sum of independent zero-truncated Poisson random variables

The objective of this article is to derive the density function and cumulative distribution function for random variables which may be written as the sum of independent (either identical or non-identical) zerotruncated Poisson random variables. The obtained expressions may be particularly useful for modelling purposes, especially in view of linking common purchase quantity models from the marketing literature to stochastic production-inventory models from the operations management literature.