Skellam Poisson Difference

Subtract two independent event counts and follow diagonal probability mass.

Experiment

Use the Skellam Poisson Difference interactive tool to explore the distribution of differences.

1. Set Poisson mean 1 to 2 and Poisson mean 2 to 1. Observe that the mean difference is positive and the distribution is slightly skewed.
2. Reverse the means (Poisson mean 1 = 1, Poisson mean 2 = 2). The mean difference becomes negative, and the distribution mirrors the previous state.
3. Set one of the means to 0 (e.g., Poisson mean 1 = 2, Poisson mean 2 = 0). The difference distribution becomes identical to a standard Poisson distribution since one of the random variables is always 0.