<p>In bike-sharing studies, it is common to model the time-varying demand pattern for bikes/docks throughout the day by a piece-wise constant rate function such that in each of the smaller time intervals (say, hourly), the demand is assumed to be independently and identically distributed (i.i.d.) and follow a Poisson distribution. Consequently, this assumption enables the use of the Skellam probability distribution for modeling the change in bike/dock inventory as it represents the difference between two Poisson distributions. Through extensive computational and simulation experiments, this paper aims to assess the impact of the aforementioned piece-wise constant demand assumption on the efficacy of the Skellam distribution for modeling inventory dynamics over time. More specifically, a discrete event simulation model is developed to mimic the underlying time-varying demand for bikes and docks in a given time window. A series of nonparametric statistical tests are then used to compare the distribution of simulated bike inventory data with estimates obtained via direct sampling from the corresponding Skellam distribution parameterized based on the mean bike/dock demand rate for the assumed i.i.d. Poisson processes. The results contribute to bike-sharing research and practice by illustrating potential pitfalls and important considerations when using the Skellam probability distribution for modeling bike inventory dynamics over time under time-varying demand for bikes and docks. Without the formal statistical analysis presented in this paper, there is a risk of inappropriate use of the Skellam probability distribution in modeling inventory dynamics, affecting the statistical validity of future models and research findings related to bike-sharing systems.</p>