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Asymptotic approximations of expectations of power means

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  • Tomislav Burić
  • Lenka Mihoković

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.

Suggested Citation

  • Tomislav Burić & Lenka Mihoković, 2024. "Asymptotic approximations of expectations of power means," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(3), pages 505-522, August.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:3:p:505-522
    DOI: 10.1111/stan.12331
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