Tail bounds for sums of independent two-sided exponential random variables

TL;DR

This paper derives tight upper and lower bounds for the tail probabilities of weighted sums of two-sided exponential variables, extending previous results from one-sided to two-sided cases.

Contribution

It provides the first comprehensive tail bounds for sums of two-sided exponential variables, matching the leading terms and extending prior work on one-sided exponentials.

Findings

Established tight bounds for tail probabilities of two-sided exponential sums.

Extended Janson's results from one-sided to two-sided exponential distributions.

Provided analytical tools for analyzing sums of two-sided exponential variables.

Abstract

We establish upper and lower bounds with matching leading terms for tails of weighted sums of two-sided exponential random variables. This extends Janson's recent results for one-sided exponentials.