Sharp Rosenthal-type inequalities for mixtures and log-concave variables

TL;DR

This paper derives sharp Rosenthal-type inequalities with optimal constants for sums of independent mixture variables and identifies extremisers in log-concave contexts under moment constraints.

Contribution

It introduces new sharp inequalities for mixture distributions and characterizes extremisers in log-concave settings, advancing understanding of moment bounds.

Findings

Sharp constants for Rosenthal-type inequalities derived

Extremisers identified in log-concave distribution settings

Enhanced bounds for moments of mixture variables

Abstract

We obtain Rosenthal-type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremisers in log-concave settings when the moments of summands are individually constrained.