# When Lorenz met Lyapunov

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.
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Journal articles

https://hal-hec.archives-ouvertes.fr/hal-00540204
Contributor : Antoine Haldemann Connect in order to contact the contributor
Submitted on : Friday, November 26, 2010 - 10:17:05 AM
Last modification on : Saturday, June 25, 2022 - 10:51:31 AM

### Citation

Marco Scarsini, Marco Dall'Aglio. When Lorenz met Lyapunov. Statistics and Probability Letters, Elsevier, 2001, Vol. 54, N°1, pp. 101-105. ⟨10.1016/S0167-7152(01)00084-0⟩. ⟨hal-00540204⟩

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