When Lorenz met Lyapunov

M. Dall'Aglio, M. SCARSINI

Statistics & Probability Letters

2001, vol. 54, n°1, pp.101-105

Départements : Economie et Sciences de la décision

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