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We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of examples under certain regularity conditions like log-convexity. Moreover, we derive concentration bounds for polynomial chaos of any order d.

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Some Notes on Moment Inequalities for Heavy-Tailed Distributions

  • 会议论文

  • 发表日期：

    2026年

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  • Paul Buterus,
  • Holger Sambale

摘要

We investigate the relation between moments and tails of heavy-tailed (in particular, Pareto-type) distributions. We also discuss the sharpness of our results in a number of examples under certain regularity conditions like log-convexity. Moreover, we derive concentration bounds for polynomial chaos of any order d.