cumulative distribution function

Let X be a random variableMathworldPlanetmath. Define FX:R[0,1] as FX(x)=Pr[Xx] for all x. The functionMathworldPlanetmath FX(x) is called the cumulative distribution functionMathworldPlanetmathPlanetmathPlanetmath of X.

Every cumulative distribution function satisfies the following properties:

  1. 1.

    limx-FX(x)=0 and limx+FX(x)=1,

  2. 2.

    FX is a monotonically nondecreasing function,

  3. 3.

    FX is continuous from the right,

  4. 4.


If X is a discrete random variable, then the cumulative distributionDlmfPlanetmath can be expressed as FX(x)=kxPr[X=k].

Similarly, if X is a continuous random variable, then FX(x)=-xfX(y)𝑑y where fX is the density distribution function.

Title cumulative distribution function
Canonical name CumulativeDistributionFunction
Date of creation 2013-03-22 11:53:38
Last modified on 2013-03-22 11:53:38
Owner bbukh (348)
Last modified by bbukh (348)
Numerical id 10
Author bbukh (348)
Entry type Definition
Classification msc 60A99
Classification msc 46L05
Classification msc 82-00
Classification msc 83-00
Classification msc 81-00
Related topic DistributionFunction
Related topic DensityFunction