Asymptotic approximations of expectations of power means

Author:

Burić Tomislav1,Mihoković Lenka1ORCID

Affiliation:

1. Faculty of Electrical Engineering and Computing University of Zagreb Zagreb Croatia

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 nonnegative 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 behavior depending on sample size contributes to interesting connections with the power mean of probability distribution.

Publisher

Wiley

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

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