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

What the math gives to ML

The paper gives a constructive ordering principle for a family of discrete count distributions: after reparameterizing by their common mean, a monotone ratio condition on the death-rate sequences guarantees convex-order dominance. This is stronger than matching only variance, because every convex tail-sensitive functional is ordered simultaneously. The most direct neural-network transfer is a count-output head with an explicit mean-preserving dispersion parameter, using the ordering theorem to constrain or regularize predicted distributions without changing their expected count. The idea is especially natural for event-count, reliability, traffic, and overdispersed target distributions.