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Upper bounds for the tail of the compound negative binomial distribution

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  • Gordon E. Willmot
  • Xiaodong Lin

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.

Suggested Citation

  • Gordon E. Willmot & Xiaodong Lin, 1997. "Upper bounds for the tail of the compound negative binomial distribution," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 1997(2), pages 138-148.
    • Handle: RePEc:taf:sactxx:v:1997:y:1997:i:2:p:138-148
    DOI: 10.1080/03461238.1997.10413983
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