Subexponential distribution functions
- 1 May 1980
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 29 (3), 337-347
- https://doi.org/10.1017/s1446788700021340
Abstract
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.Keywords
This publication has 5 references indexed in Scilit:
- The Class of Subexponential DistributionsThe Annals of Probability, 1975
- On the tails of waiting-time distributionsJournal of Applied Probability, 1975
- Degeneracy Properties of Subcritical Branching ProcessesThe Annals of Probability, 1973
- Branching ProcessesPublished by Springer Nature ,1972
- A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Random ProcessesTheory of Probability and Its Applications, 1964