An inequality involving alternating binomial sums

Abstract

In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was introduced in our recent work [On the minimum of independent collecting processes via the Stirling numbers of the second kind, Statist. Probab. Lett., 185 (2022)].