the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value. It can be view as the inverse of the cumulative distribution function.
It is also called the percentile function (after percentile), percent-point function, inverse cumulative distribution function or inverse distribution function.
Given a random variable
The quantile function will be
Graphically, we can understand the quantile function as given an area
Related
- inverse transform sampling - Using quantile function to sample numbers from a distribution