ThmDex – An index of mathematical definitions, results, and conjectures.
▼ Set of symbols
▼ Alphabet
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▼ Zermelo-Fraenkel set theory
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▼ Unsigned basic measure
▼ Borel measure
▼ Set of borel measures
▼ Set of borel probability measures
▼ Stochastic dominance relation
Definition D5324
Random real number stochastic ordering relation
Formulation 0
Let $\mathcal{R} : = \text{Random}(\mathbb{R})$ be the D5721: Class of random basic real numbers.
The stochastic ordering relation is the D4: Binary relation \begin{equation} {\preceq} : = \left\{ (X, Y) \in \mathcal{R} \times \mathcal{R} \mid \forall \, t \in \mathbb{R} : \mathbb{P}(X \leq t) \geq \mathbb{P}(Y \leq t) \right\} \end{equation}
Also known as
Random real number stochastic dominance relation