ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Statistics and Probability: Cumulative Distribution Function

Updated on October 30, 2019
Patty Inglish, MS profile image

Ms. Inglish has 30 years of success in medicine, psychology, STEM instruction, and aerospace education for Active USAF Civil Air Patrol.

What is a Cumulative Distribution Function and how do we calculate, produce, and use the data provided by such a distribution?
What is a Cumulative Distribution Function and how do we calculate, produce, and use the data provided by such a distribution? | Source

Statistics is a Fascinating Field of Study

Statistics are important because the study can help us learn about our universe and the things and beings in it. This is an even more important capability in the face of our flying back to the moon in or before 2018. Trigonometry, calculus, and statistics all help us to fly away from Earth, visit other places, and return.

These divisions of mathematics help us to build bridges as well as to construct bio-robotic arms and legs to replace those loss in battle or lost to injury or genetic events.

Because our universe, though we think it is never ending, has some sort of boundary, numbers behave in a particular number of ways. We have not yet found that number, but we know that equations and distributions are bound by limits concerning results and that the laws of physics for this universe also have boundaries. Quantum physics, not so much, perhaps.

Prediction and Analysis

Statistics and Probability help us to predict and to plan in several fields of study and many industries. They are useful in Aerospace, Engineering, Health & Medical, Information Technology, and many other endeavors.

Statistical Resources

What is a Cumulative Distribution Function and how does one calculate, produce, and use the information provided by such a distribution?

This particular distribution function is also known as a CDF, cumulative distribution function, or cumulative frequency function (CFF). Its purpose is to provide the probability that a variable takes on a value that is less-than-or-equal-to a particular number.

A good reference for understanding CDF and CFF is that of Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 4rd ed. New York: Wiley, pp. 6-8, 2000/2010.

Along the right-hand side of this article, you will find various computer programs used for running the CDF. It is difficult, if not impossible to achieve CDF outcomes by hand figuring and hand graphing. A computer program is necessary.

Texts and Manuals

An abundance of statistics texts and manuals, as well as hand held statistical and graphing computers are available on the market to enable students and researchers to use the CDF and other complex functions easily and quickly.

Additional Useful Statistics Resources

Several additional resources can be accessed for use in determining and applying the CDF in real life scenarios. Some of these resources include:

  • Engineers Handbook: This is one of my favorite resources. My father studied mechanical and electrical engineering and always kept an edition of this book on hand. I found it very useful in high school for trigonometry and calculus reference, and was fascinated by all of the tables it included.
  • FedStats: Statistics and additional data provided by various departments of the US Federal Government. Excellent for research and reviews.
  • HYPERSTAT: Simple introduction to statistics.
  • MATLab: A comprehensive set of statistics tools that are used by engineers, financial analysts, and others.
  • Robert Niles: Statistics for journalists.
  • Statistics on The Library Spot: Statistics from a range of various government bureaus.
  • For additional resources, visit you nearest college or university mathematics or engineering department library and review the software programs on public-access computers.

Understanding Distributions


Cumulative Distribution Function of the Standard Normal Distribution

A good reference for this distribution is the Engineering Statistics Handbook. Tests for Probability of Distribution: Cumulative Distribution Function of the Standard Normal Distribution. US Department of Commerce: NIST

NOTE: The table on this federal internet page applies the symmetry of the normal distribution, so the relevant expression for the variable of interest given is really the following:

This is another useful software program to use for the CDF: Jenness Enterprises Software.
This is another useful software program to use for the CDF: Jenness Enterprises Software. | Source

This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.

© 2007 Patty Inglish MS


    0 of 8192 characters used
    Post Comment
    • Patty Inglish, MS profile imageAUTHOR

      Patty Inglish MS 

      12 years ago from USA and Asgardia, the First Space Nation

      The status of multiple formulae or a non-closed or open formula(s) or one or more formula set(s) is a given; along with other mathematic precepts. I listed more than one software program for performing the function and each uses its own 'programming' and formula/ formulae. I did not compare the programs and formula(s), because I leave that up to the user or student needing to answer the question of the request.

      As a quirky side note, in research some time ago, I attempted to hand construct a curve from a fractal function and was able to plot only 3 points aver a few hours. Computer use is the most practical application for certain functions.

      Thanks for the comment.

    • Maddie Ruud profile image

      Maddie Ruud 

      12 years ago from Oakland, CA

      My father is an econometrician, and he says this:

      "You can't. You need a computer program. There is no closed formula."

      At least that is my simplification of the stream of math-jargon that came out of his mouth when I read this request aloud to him on my last visit.

    • Patty Inglish, MS profile imageAUTHOR

      Patty Inglish MS 

      12 years ago from USA and Asgardia, the First Space Nation

      Well, I know how to put together my notes and experiences and how to look things up. So, maybe one day...

      Thanks for the comment!

    • Earth Angel profile image

      Earth Angel 

      12 years ago

      Wow!! You are GREAT Patty!! Have you ever thought of publishing your own book?? I am a huge proponent of self-publishing!! Your Hubs are always full of wonderful and helpful information!! Thank you!! Blessings, Earth Angel!!


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)