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Extreme values of scaled L-moments

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  • Rychlik, Tomasz
  • Szymkowiak, Magdalena

Abstract

Due to Hosking (1990) (J. R. Stat. Soc. Ser. B Stat. Methodol.52, 105–124) all the values of scaled L-moments belong to the interval (−1,1). We prove that 1 is actually the sharp upper bound for every scaled L-moment, and −1 is the optimal lower bound for the odd scaled L-moments. We present a method of determining the optimal lower bounds on even scaled L-moments, which are located in (−1,0). We also present sharp lower and upper bounds on the L-moments based on nonnegative samples and measured in the units being the expectations of the parent distributions.

Suggested Citation

  • Rychlik, Tomasz & Szymkowiak, Magdalena, 2026. "Extreme values of scaled L-moments," Statistics & Probability Letters, Elsevier, vol. 231(C).
    • Handle: RePEc:eee:stapro:v:231:y:2026:i:c:s0167715225002718
    DOI: 10.1016/j.spl.2025.110626
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    References listed on IDEAS

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    1. Kerstens, Kristiaan & Mounir, Amine & de Woestyne, Ignace Van, 2011. "Non-parametric frontier estimates of mutual fund performance using C- and L-moments: Some specification tests," Journal of Banking & Finance, Elsevier, vol. 35(5), pages 1190-1201, May.
    2. Jones, M.C. & Balakrishnan, N., 2025. "On absolute moment-based upper bounds for L-moments," Statistics & Probability Letters, Elsevier, vol. 216(C).
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