A distribution function (F on [0,∞) belongs to the subexponential class if and only if 1−F(2) (x) ~ 2(1−F(x)), as x→ ∞. For an important class of distribution functions, a simple, necessary and sufficient condition for membership of is given. A comparison theorem for membership of and also some closure properties of are obtained.
1980 Mathematics subject classification (Amer. Math. Soe.): primary 60 E 05; secondary 60 J 80.
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