Quantile

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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 $\alpha \leq F(x)$

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