Improved Inequalities for the Poisson and Binomial Distribution and Upper Tail Quantile Functions

Figure 1

Comparison of the exact (blue) and bounded (green) number of arrivals versus time 𝑡, for a Poisson process having intensity 𝜆=0.1 for confidence probabilities 𝑅=(1−10⁻⁵) and 𝑅=(1−10⁻⁹).