Moment-Ratio Diagrams for Univariate Distributions

Erik Vargo, Raghu Pasupathy and Lawrence M. Leemis ()
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Erik Vargo: MITRE
Raghu Pasupathy: Purdue University
Lawrence M. Leemis: The College of William and Mary

Chapter 12 in Computational Probability Applications, 2017, pp 149-164 from Springer

Abstract: Abstract We present two moment-ratio diagrams along with guidance for their interpretation. The first moment-ratio diagram is a graph of skewness vs. kurtosis for common univariate probability distributions. The second moment-ratio diagram is a graph of coefficient of variation vs. skewness for common univariate probability distributions. Both of these diagrams, to our knowledge, are the most comprehensive to date. The diagrams serve four purposes: (1) they quantify the proximity between various univariate distributions based on their second, third, and fourth moments, (2) they illustrate the versatility of a particular distribution based on the range of values that the various moments can assume, (3) they can be used to create a short list of potential probability models based on a data set, and (4) they clarify the limiting relationships between various well-known distribution families. The use of the moment-ratio diagrams for choosing a distribution that models given data is illustrated.

Keywords: Coefficient of variation; Kurtosis; Skewness (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/978-3-319-43317-2_12

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