Uniform stochastic ordering and related inequalities

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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.

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