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We cardinally and ordinally rank distribution functions (CDFs). We present anew class of statistics, maximal adjusted quantiles, and show that a statisticis invariant with respect to cardinal shifts, preserves least upper bounds withrespect to the first order stochastic dominance relation, and is lowersemicontinuous if and only if it is a maximal adjusted quantile. A dual resultis provided, as are ordinal results. Preservation of least upper bounds isgiven several interpretations, including one that relates to changes in taxbrackets, and one that relates to valuing options composed of two assets.

Multiple Adjusted Quantiles