Cumulative Distribution Function

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.

REFERENCE:

Evans, M.; Hastings, N.; and Peacock, B. Statistical Distributions, 3rd ed. New York: Wiley, pp. 6-8, 2000.

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.

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. Using this online version, click on a tab at the top of the page for Reference Tables. I think you will be pleased at the extensive material you find in this book.
• 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.
• Statistics on The Library Spot - Statistics from a range of various government bureaus.
• Robert Niles - Statistics for journalists.
• For additional resources, visit you nearest college or university mathematics or engineering department library and review the software programs on public-access computers.

REFERENCE:

Engineering Statistics Handbook. 1.3.6.7.1: Tests for Probability of Distribution: Cumulative Distribution Function of the Standard Normal Distribution. US Department of Commerce: NIST

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