Sub-Weibull distributions: generalizing sub-Gaussian and sub-Exponential properties to heavier-tailed distributions
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We propose the notion of sub-Weibull distributions, which are characterised by tails lighter than (or equally light as) the right tail of a Weibull distribution. This novel class generalises the sub-Gaussian and sub-Exponential to potentially heavier-tailed distributions. Sub-Weibull distributions are parameterised by a positive tail index θ and reduce to sub-Gaussian distributions for θ=1/2 and to sub-Exponential distributions for θ=1. A characterisation of the sub-Weibull property based on moments and on the moment generating function is provided and properties of the class are studied.
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