Univariate Probability Distributions

Abstract

We describe a web-based interactive graphic that can be used as a resource in introductory classes in mathematical statistics. This interactive graphic presents 76 common univariate distributions and gives details on (a) various features of the distribution such as the functional form of the PDF and CDF, graphs of the PDF for various parameter settings, and values of population moments; (b) properties that the distribution possesses, for example, linear combinations of independent random variables from a particular distribution family also belong to the same distribution family; and (c) relationships between the various distributions, including special cases, transformations, limiting distributions, and Bayesian relationships. The interactive graphic went on-line on 11/30/12 at the URL www.math.wm.edu/ ∼ leemis/chart/UDR/UDR.html. As of May 2016, the site has had 42,000 page views from 35,000 unique visitors.

Originally published in the Journal of Statistics Education, Volume 20, Number 3 in 2012, this paper illustrates the use of APPL throughout its foundation. So much is APPL ingrained in the background work of the paper, it was not even mentioned as a reference book. Like people who crunch numbers in Excel or type papers in Word, often these two important software packages do not get mentioned in the reference section of a report. This is our vision for APPL also, that it is a tool used by researchers as part of their everyday work environment. Included at the end of this paper are two subsequent sections that have expanded the original manuscript that show the APPL verifications used in computations associated with the binomial and exponential distributions. These sections are found in the website of the diagram and highlight the APPL commands used to verify the results of this paper.