Definition: Quantile function
Index: The Book of Statistical Proofs ▷ General Theorems ▷ Probability theory ▷ Other probability functions ▷ Quantile function
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Metadata: ID: D14 | shortcut: qf | author: JoramSoch | date: 2020-02-17, 22:18.
Definition: Let $X$ be a random variable with the cumulative distribution function (CDF) $F_X(x)$. Then, the function $Q_X(p): [0,1] \to \mathbb{R}$ which is the inverse CDF is the quantile function (QF) of $X$. More precisely, the QF is the function that, for a given quantile $p \in [0,1]$, returns the smallest $x$ for which $F_X(x) = p$:
\[\label{eq:qf} Q_X(p) = \min \left\lbrace x \in \mathbb{R} \, \vert \, F_X(x) = p \right\rbrace \; .\]- Wikipedia (2020): "Probability density function"; in: Wikipedia, the free encyclopedia, retrieved on 2020-02-17; URL: https://en.wikipedia.org/wiki/Quantile_function#Definition.
Metadata: ID: D14 | shortcut: qf | author: JoramSoch | date: 2020-02-17, 22:18.