Tail bounds for sum of gamma variables and related inferences

Abstract

Svante Janson presented sharper tail bounds for sum of geometric and exponential variables. In this article, we consider for gamma variables with real number parameters and obtain similar results. As a result, more particular examples of gamma variables like exponential variables and chi-square variables can also be included in this framework.

Keywords:

• Tail bounds
• characteristic functions
• gamma variables
• binomial variables

Mathematics Subject Classification (2010):

• 60E10
• 60E15

Acknowledgments

We thank the helpful instructions from professor Zechun Hu and the useful discussions of Mr. Hongxu Chen. We are also grateful for the comments and suggestions from anonymous reviewers and editors, who correct our mistakes in this article and help a lot to improve the presentation of our paper.

Additional information

Funding

This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 20826041C4191) and the Spark Program Fund of WuYuzhang Honors College.