 The tail distribution function formula_13 is defined as formula_14.A distribution formula_8 on the positive half-line is subexponential if

This implies that, for any formula_17,

The probabilistic interpretation of this is that, for a sum of formula_19 independent random variables formula_20 with common distribution formula_8,

This is often known as the principle of the single big jump or catastrophe principle.A distribution formula_8 on the whole real line is subexponential if the distribution
formula_24 is.