Lorenz and convex ordering of parasite burden distributions with density-dependent deaths

2026/07/24 by Madison Carlton, Ross McVinish
#math.PR

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Abstract

We establish a convex ordering result for count distributions arising from a parasite acquisition model with density-dependent deaths. If the ratio of two death-rate sequences is non-increasing, then the corresponding mean-parametrised distributions are ordered in the convex order. This yields, as a special case, the convex ordering of the mean-parametrised Conway-Maxwell-Poisson distribution in its dispersion parameter.

Citations

• On Arbitrarily Underdispersed Discrete Distributions

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