A Note on Symmetric Random Vectors with an Application to Discrete Choice

University of Zurich, Department of Economics, Working Paper No. 419

22 Pages Posted: 31 Oct 2022

See all articles by Andreas Hefti

Andreas Hefti

University of Zurich - Department of Economics; Zurich University of Applied Sciences

Date Written: October 20, 2022

Abstract

This paper studies random vectors X featuring symmetric distributions in that i) the order of the random variables in X does not affect its distribution, or ii) the distribution of X is symmetric at zero. We derive a number of characterization results for such random vectors, thereby connecting the distributional symmetry to various notions of how (Euclidean) functions have been regarded as symmetric. In addition, we present results about the marginals and conditionals of symmetrically distributed random vectors, and apply some of our results to various transformations of random vectors, e.g., to sums or products of random variables, or in context of a choice probability system known from economic models of discrete choice.

Keywords: [comma sSymmetric Distributions, Symmetric Random Vectors, Symmetric Random Variables, Symmetric Functions, Choice Probability Systemeparated]

JEL Classification: C10, C44, D11

Suggested Citation

Hefti, Andreas M., A Note on Symmetric Random Vectors with an Application to Discrete Choice (October 20, 2022). University of Zurich, Department of Economics, Working Paper No. 419, Available at SSRN: https://ssrn.com/abstract=4254015 or http://dx.doi.org/10.2139/ssrn.4254015

Andreas M. Hefti (Contact Author)

University of Zurich - Department of Economics ( email )

Z├╝rich
Switzerland

Zurich University of Applied Sciences ( email )

Institut fuer Angewandte Medienwissenschaft
Zur Kesselschmiede 35
Winterthur, CH 8401
Switzerland

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