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When Lorenz met Lyapunov

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  • Dall'Aglio, Marco
  • Scarsini, Marco

Abstract

We provide a simple characterization of the zonoid, lift zonoid, Lorenz zonoid of a random vector, as defined by Koshevoy and Mosler (J. Amer. Statist. Assoc. 91 (1996) 873; Bernoulli 4 (1998) 377). This characterization allows a direct use of Lyapunov's theorem on the range of nonatomic vector measures and therefore simplifies the proof of some results.

Suggested Citation

  • Dall'Aglio, Marco & Scarsini, Marco, 2001. "When Lorenz met Lyapunov," Statistics & Probability Letters, Elsevier, vol. 54(1), pages 101-105, August.
    • Handle: RePEc:eee:stapro:v:54:y:2001:i:1:p:101-105
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    Cited by:

    1. Marco Dall’Aglio & Marco Scarsini, 2000. "Zonoids, Linear Dependence, and Size-Biased Distributions on the Simplex," ICER Working Papers - Applied Mathematics Series 27-2003, ICER - International Centre for Economic Research, revised Jul 2003.
    2. Karl Mosler, 2003. "Central Regions and Dependency," Methodology and Computing in Applied Probability, Springer, vol. 5(1), pages 5-21, March.

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