= Subexponential distribution
{disambiguate=heavy-tailed}
{title2=$\mathbb P(X_1+X_2>x)\sim2\mathbb P(X_1>x)$}
= Heavy-tailed subexponential distribution
{synonym}
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 $1-F(x)^2\sim2\overline F(x)$, 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.
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