An optimal upper bound on the tail probability for sums of random variables

Authors

Iosif Pinelis, Michigan Technological UniversityFollow

Document Type

Article

Publication Date

10-22-2019

Department

Department of Mathematical Sciences

Abstract

Let $s$ be any given real number. An explicit construction is provided of random variables (r.v.'s) $X$ and $Y$ such that $\sup{P}(X+Y\ge s)$ is attained, where the $\sup$ is taken over all r.v.'s $X$ and $Y$ with given distributions.

Publication Title

Theory of Probability & Its Applications

Recommended Citation

Pinelis, I. (2019). An optimal upper bound on the tail probability for sums of random variables. Theory of Probability & Its Applications, 64(3), 474-480. http://doi.org/10.1137/S0040585X97T989635
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/1175