A Note on Over- and Under-Representation Among Populations with Normally-Distributed Traits

Publication date: 16 March 2021

Abstract: In every finite mixture of different normal distributions, there will always be exactly one of those distributions that not only is over-represented in the right tail of the mixture, but even completely overwhelms all other subpopulations in the rightmost tails. This property, although not unique to normal distributions, is not shared by other common continuous centrally-symmetric unimodal distributions such as Laplace, nor even by other bell-shaped distributions such as Cauchy (Lorentz) distributions.

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Statistics of extreme values; tail inference (62G32) Probability distributions: general theory (60E05) Population dynamics (general) (92D25)

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