Discrete s-convex extremal distributions: theory and applications
(2005)
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- Abstract
- Given a nondegenerated moment space with s fixed moments, explicit formulas for the discrete s- convex extremal distribution have been derived for s = 1, 2, 3 (see [1]). If s = 4, only the maximal distribution is known (see [2]). This paper goes beyond this limitation and proposes a method to derive explicit expressions for general nonnegative integer s. In particular, we derive explicitly the discrete 4-convex minimal distribution. For illustration, we show how this theory allows to bound the probability of extinction in a Galton-Watson branching process. The results are also applied to derive bounds for the probability of ruin in the compound binomial and Poisson insurance risk models.
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Citations
Courtois, C., Denuit, M., & Van Bellegem, S. (2005). Discrete s-convex extremal distributions: theory and applications (STAT Discussion Paper 0529). https://hdl.handle.net/2078.5/160443