Abstract

A real random variable admits median(s) and quantiles. These values minimize convex functions on the reals R. This is known. We discuss these results and their relationship with some notions about functions of bounded variation developed by J. J. Moreau in his mathematical work in view of the mechanical phenomena which are shocks and friction, especially filled-in graphs and Stieltjes measures of products of BV functions.

Author information

Contact details are reproduced from the original publication and may be historical.

Michel Valadier

IMAG, Université Montpellier II, Place Eugène Bataillon, Case Courier 051,
34095 Montpellier Cedex, France

mivaladier@wanadoo.fr

Keywords

  • Median
  • quantile
  • convexity
  • subdifferential
  • monotone operator
  • minimizer
  • BV function

Mathematics Subject Classification

62E99, 52A99

Suggested citation

M. Valadier. “Quantiles and Convexity.” Journal of Convex Analysis 23 (2016), No. 4, 1125–1136.

Copyright Heldermann Verlag 2016