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 and , the CDF finds given and the quantile function finds given . In other word, if we have a CDF

The quantile function will be

1

Graphically, we can understand the quantile function as given an area , what is the value such that the CDF is equal to that area. qnorm.png

Footnotes

  1. Quantile function - Wikipedia