Tail bounds for weighted sums of independent Poisson random variables

Abstract

In this article, we provide the recursive inequalities for weighted sums of Poisson random variables. Furthermore, we establish their upper and lower bounds. Some numerical simulations are also demonstrated. Particularly, in some cases, we demonstrate that our bounds are sharper than the ones in Pelekis (2016) by numerical results.

Keywords:

• Tail probabilities
• Poisson random variables
• weighted sums
• the moment generating function

2010 MSC::

• 60F15

Acknowledgments

The authors are very grateful to the reviewers for the valuable comments and suggestions in the early draft.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was supported by the National Key R&D Program of China (No. 2023YFA1009200), the National Natural Science Foundation of China (Grant No. 12371154), the Fundamental Research Funds for the Central Universities (DUT23LAB307), and the Dalian High-level Talent Innovation Program (Grant No. 2020RD09). The third author was partially supported by the National Natural Science Foundation of China (Grant No. 12101104).