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}

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Function

▾ Measure

▾ Real measure

▾ Euclidean real measure

▾ Complex measure

▾ Basic measure

▾ Unsigned basic measure

▾ Borel measure

▾ Set of borel measures

▾ Set of borel probability measures

▾ Stochastic dominance relation

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Function

▾ Measure

▾ Real measure

▾ Euclidean real measure

▾ Complex measure

▾ Basic measure

▾ Unsigned basic measure

▾ Borel measure

▾ Set of borel measures

▾ Set of borel probability measures

▾ Stochastic dominance 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}

The

Also known as

Random real number stochastic dominance relation

Results