Hi Clément,
It seems that the bound of the Poisson tail inequality can be further improved. In the current version of this note, it is shown that $\Pr(|x - \lambda| \geq x) \leq \exp\left(-\frac{x^2}{2(\lambda + x)}\right)$. However, we propose a slightly improved bound: $\Pr(|x - \lambda| \geq x) \leq \exp\left(-\frac{x^2}{2\lambda + x}\right)$. Proof of this improved bound is provided in Appendix B here.
Hi Clément,
It seems that the bound of the Poisson tail inequality can be further improved. In the current version of this note, it is shown that$\Pr(|x - \lambda| \geq x) \leq \exp\left(-\frac{x^2}{2(\lambda + x)}\right)$ . However, we propose a slightly improved bound: $\Pr(|x - \lambda| \geq x) \leq \exp\left(-\frac{x^2}{2\lambda + x}\right)$ . Proof of this improved bound is provided in Appendix B here.