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.