ON THE RELATIONSHIP BETWEEN BOUNDS ON THE TAILS OF COMPOUND DISTRIBUTIONS

Authors
WILLMOT GE
Citation
Ge. Willmot, ON THE RELATIONSHIP BETWEEN BOUNDS ON THE TAILS OF COMPOUND DISTRIBUTIONS, Insurance. Mathematics & economics, 19(2), 1997, pp. 95-103
Citations number
9
Categorie Soggetti
Social Sciences, Mathematical Methods",Economics,"Mathematical, Methods, Social Sciences","Mathematics, Miscellaneous","Statistic & Probability
Journal title
Insurance. Mathematics & economics → ACNP
ISSN journal
01676687
Volume
19
Issue
2
Year of publication
1997
Pages
95 - 103
Database
ISI
SICI code
0167-6687(1997)19:2<95:OTRBBO>2.0.ZU;2-P
Abstract
A comparison of two upper bounds for the tails of compound distributio ns, both defined in terms of a new worse than used (NWU) distribution, reveals that one is sharper in the decreasing failure rate (DFR) case . An inductive argument is employed to construct a lower bound in term s of a new better than used (NBU) distribution which is a dual to the upper bound. It is also sharper than the corresponding lower bound in the increasing failure rate (IFR) case. Applications to ruin theory ar e then given.