Univariate Probability Distributions

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...

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Bibliographic Details
Published inComputational Probability Applications Vol. 247; pp. 133 - 147
Main Authors Leemis, Lawrence M., Luckett, Daniel J., Powell, Austin G., Vermeer, Peter E.
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2017
Springer International Publishing
SeriesInternational Series in Operations Research & Management Science
Subjects
Continuous distributions
Discrete distributions
Distribution properties
Limiting distributions
Mathematical & statistical software
Operational research
Probability & statistics
Special cases
Transformations
Univariate distributions
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Summary: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.
Bibliography: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.
ISBN:3319433156
9783319433158
ISSN:0884-8289
2214-7934
DOI:10.1007/978-3-319-43317-2_11