A distribution function F on (0,•) belongs to the subexponential class 𝒮 if the ratio of 1-F’(2’)(x) to 1-F(x) converges to 2 as x⇒•. A necessary condition for membership in 𝒮 is used to prove that a certain class of functions previously thought to be contained in 𝒮 has members outside of 𝒮. Sufficient conditions on the tail of F are found which ensure F belongs to 𝒮; these conditions generalize previously published conditions.
