English

Non-comparability with respect to the convex transform order with applications

Probability 2019-09-09 v1

Abstract

In the literature of stochastic orders, one rarely finds results that can be considered as criteria for the non-comparability of random variables. In this paper, we provide results that enable researchers to use simple tools to conclude that two random variables are not comparable with respect to the convex transform order. The criteria are applied to prove the non-comparability of parallel systems with components that are either exponential, Weibull or Gamma distributed, providing a negative answer for a conjecture about comparability with respect to the convex transform order in a much broader scope than its initial statement.

Keywords

Cite

@article{arxiv.1909.03024,
  title  = {Non-comparability with respect to the convex transform order with applications},
  author = {Idir Arab and Milto Hadjikyriakou and Paulo Eduardo Oliveira},
  journal= {arXiv preprint arXiv:1909.03024},
  year   = {2019}
}
R2 v1 2026-06-23T11:08:02.207Z