9827

Convergence of the Empirical Distribution Function of a Sample

The empirical distribution function (EDF) of a random sample is the cumulative distribution function of the values obtained in the sample. You would intuitively expect the EDF to resemble the cumulative distribution function of the parent distribution (that is, the distribution the sample is drawn from).
This idea is formalized in the Glivenko-Cantelli theorem (also called the fundamental theorem of statistics), which states that the EDF converges pointwise to the parent distribution.
This result is illustrated here for three different parent distributions: the normal distribution with parameters (0, 1), the uniform distribution with parameters (-5, 5), and the gamma distribution with parameters (2, 0.6). You can see the EDF of a random sample approach the parent distribution as the sample size increases.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+