---
title: "Cumulative distribution function - cdf"
canonical: "https://modelassist.epixanalytics.com/space/EA/26574886/Cumulative%20distribution%20function%20-%20cdf"
format: markdown
---
The (cumulative) distribution function, or *probability distribution function*, *F*(*x*) is the mathematical equation that describes the probability that a variable *X* is less that or equal to *x*, i.e.


     *F*(*x*) = *P*(*X*≤*x*)                    for all *x*


where *P*(*X*≤*x*) means the probability of the event *X*≤*x*.


A cumulative distribution function has the following properties:

1.    *F(x)* is always non-decreasing, i.e. > Macro (inline-media-image)



> Macro (mathinline)



2.    *F*(*x*) = 0 at *x* = -∞ or minimum

*     F*(*x*) = 1 at *x* = ∞ or maximum




---