Asymptotic approximations of expectations of power means

Abstract In this paper we study how the expectations of power means behave asymptotically as some relevant parameter approaches infinity and how to approximate them accurately for general non‐negative continuous probability distributions. We derive approximation formulae for such expectations as distribution mean increases, and apply them to some commonly used distributions in statistics and financial mathematics. By numerical computations we demonstrate the accuracy of the proposed formulae which behave well even for smaller sample sizes. Furthermore, analysis of behaviour depending on sample size contributes to interesting connections with the power mean of probability distribution. This article is protected by copyright. All rights reserved.