Inequalities and comparisons of the Cauchy, Gauss, and logistic distributions

摘要

In this note, some inequalities and basic results including characterizations and comparisons of the Cauchy, logistic, and normal distributions are given. These results lead to necessary and sufficient conditions for the stochastic and dispersive ordering of the corresponding absolute random variables. (C) 2004 Elsevier Ltd. All rights reserved. [References: 2]