๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Upper bounds for the tail of the compound negative binomial distribution

โœ Scribed by E.G. Willmot; X. Lin

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
105 KB
Volume
22
Category
Article
ISSN
0167-6687

No coin nor oath required. For personal study only.

โœฆ Synopsis

A general upper bound for the tail of the compound negative binomial distribution is constructed. By establishing a connection with the individual risk mode the upper bound is seen to be a (possibly degenerate) mixture of tails of gamma distribution. The bound is sharp in that it is an equality in the compound Pascal-exponential case. Two important special cases of the bound are derived. The issue of construction of an optimal upper bound is considered.

๐Ÿ“œ SIMILAR VOLUMES

On the relationship between bounds on th
On the relationship between bounds on the tails of compound distributions
โœ Gordon E. Willmot ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 338 KB

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 th