 Subexponential distribution (heavy-tailed)

For nonnegative independent and identically distributed random variables with unbounded support, this is the displayed two-summand tail asymptotic. The probability that the maximum exceeds $x$ is $1-F(x{)}^2\sim 2\overline{F}(x)$, so the sum and maximum have asymptotically the same tail. This is the basic single-large-arrival effect relevant to queue overflow. The concentration-theory sub-exponential random variable uses a separate light-tail convention.