---
tag: 0X60VE98HN
kind: concept
name: Quantile function
aliases: [inverse-distribution-function, percent-point-function]
msc: ["60E05"]
sources:
  - url: https://en.wikipedia.org/wiki/Quantile_function
    locator: lead section
same_as:
  wikidata: Q3489473
  wikipedia: Quantile function
---

## Summary

The quantile function of a real distribution is a generalized inverse of its cumulative distribution function.
For a level $p$ between $0$ and $1$, it gives the smallest value $x$ with probability at least $p$ of not being exceeded. The node [[quantile function|0B3Q3XDM5X]] gives the precise definition.