Some notes on moment inequalities for heavy-tailed distributions

2023/08/28 by Buterus, Paul, Sambale, Holger
#46N30 #60F10 #FOS: Mathematics #Primary 60E15 #Probability (math.PR) #Secondary 46E30

paper · doi:10.48550/arxiv.2308.14410

Abstract

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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