Skip to main content
×
×
Home

Zonoids, linear dependence, and size-biased distributions on the simplex

  • Marco Dall'Aglio (a1) and Marco Scarsini (a2)
Abstract

The zonoid of a d-dimensional random vector is used as a tool for measuring linear dependence among its components. A preorder of linear dependence is defined through inclusion of the zonoids. The zonoid of a random vector does not characterize its distribution, but it does characterize the size-biased distribution of its compositional variables. This fact will allow a characterization of our linear dependence order in terms of a linear-convex order for the size-biased compositional variables. In dimension 2 the linear dependence preorder will be shown to be weaker than the concordance order. Some examples related to the Marshall-Olkin distribution and to a copula model will be presented, and a class of measures of linear dependence will be proposed.

Copyright
Corresponding author
Postal address: Dipartimento di Scienze, Università d'Annunzio, Viale Pindaro 42, I-65127 Pescara, Italy.
∗∗ Postal address: Dipartimento di Statistica e Matematica Applicata, Università di Torino, Piazza Arbarello 8, I-10122 Torino, Italy. Email address: marco.scarsini@unito.it
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords

MSC classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 10 *
Loading metrics...

Abstract views

Total abstract views: 95 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 18th August 2018. This data will be updated every 24 hours.