Upper bounds for the tail of the compound negative binomial distribution

Gordon E. Willmot and Xiaodong Lin

Scandinavian Actuarial Journal, 1997, vol. 1997, issue 2, 138-148

Abstract: 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 distributions. 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.

Date: 1997
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DOI: 10.1080/03461238.1997.10413983

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