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Some new results on the subexponential class
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- Journal:
- Journal of Applied Probability / Volume 26 / Issue 4 / December 1989
- Published online by Cambridge University Press:
- 14 July 2016, pp. 892-897
- Print publication:
- December 1989
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- Article
- Export citation
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A distribution function F on (0,∞) belongs to the subexponential class
if the ratio of 1 – F(2)(x) to 1 – F(x) converges to 2 as x →∞. A necessary condition for membership in 
is used to prove that a certain class of functions previously thought to be contained in 
has members outside of 
. Sufficient conditions on the tail of F are found which ensure F belongs to 
; these conditions generalize previously published conditions.
if the ratio of 1 – 
is used to prove that a certain class of functions previously thought to be contained in 
has members outside of 
. Sufficient conditions on the tail of 
; these conditions generalize previously published conditions.