Quantile

Definition

The Quantile (more generaly the quantile function) associated with a probability distribution of a random variable is the value $Q$ of the Random Variable such that the probability of the variable being less than or equal to that value $Q$ equals a given probability $\alpha$

Formula

For a distribution $F(x)$, the quantile is the greatest element $x\in \mathbb{R}$ such that $\alpha \le F(x)$

$Q(\alpha) \,=\,\inf\left\{ x\in \mathbb{R} : \alpha \le F(x) \right\}$