Quantile function

In probability and statistics, a probability distribution's quantile function is the inverse of its cumulative distribution function. That is, the quantile function of a distribution ${\displaystyle {\mathcal {D}}}$ is the function ${\displaystyle Q}$ such that ${\displaystyle \Pr \left[\mathrm {X} \leq Q(p)\right]=p}$ for any random variable ${\displaystyle \mathrm {X} \sim {\mathcal {D}}}$ and probability ${\displaystyle p\in (0,1)}$.

The quantile function is also called the percentile function (after the percentile), percent-point function, inverse cumulative distribution function or inverse distribution function.