ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F11599 on D2898: Random real number percentile
F11599
Formulation 2
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number.
A D993: Real number $x \in \mathbb{R}$ is a percentile for $X$ with respect to $p \in [0, 1]$ if and only if
(1) \begin{equation} \mathbb{P}(X \leq x) \geq p \end{equation}
(2) \begin{equation} \mathbb{P}(X \geq x) \geq 1 - p \end{equation}