Uniform stochastic ordering and related inequalities

Abstract

Abstract Stochastic order between univariate random variates may be called uniform when such order persists under conditioning to a broad family of intervals. The ordering is local when it holds for any finite interval ( a, b ), however small. Local order in multivariate settings has been described by Whitt (1980, 1981), by Karlin and Rinott (1980), and by others. The prevalence of uniform and local order in a variety of simple stochastic‐process settings is displayed, and inequalities arising from such orderings developed.