✦ LIBER ✦

On the relationship between bounds on the tails of compound distributions

✍ Scribed by Gordon E. Willmot

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 338 KB
Volume: 19
Category: Article
ISSN: 0167-6687
DOI: 10.1016/s0167-6687(96)00013-3

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✦ Synopsis

A comparison of two upper bounds for the tails of compound distributions, 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 terms 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 are then given.

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