Moment-Ratio Diagrams for Univariate Distributions

We present two moment-ratio diagrams along with guidance for their interpretation. The first moment-ratio diagram is a graph of skewness versus kurtosis for common univariate probability distributions. The second moment-ratio diagram is a graph of coefficient of variation versus skewness for common...

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Bibliographic Details
Published in:Journal of quality technology 2010-07, Vol.42 (3), p.276-286
Main Authors: Vargo, Erik, Pasupathy, Raghu, Leemis, Lawrence
Format: Article
Language:English
Subjects:
Coefficient of Variation
Constraining
Control charts
Distribution theory
Exact sciences and technology
Frequency distribution
Graphs
Kurtosis
Lists
Mathematics
Normal distribution
Probability and statistics
Proximity
Random variables
Sciences and techniques of general use
Skewness
Statistics
Studies
Versatility
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Summary:We present two moment-ratio diagrams along with guidance for their interpretation. The first moment-ratio diagram is a graph of skewness versus kurtosis for common univariate probability distributions. The second moment-ratio diagram is a graph of coefficient of variation versus 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.
ISSN:0022-4065
2575-6230
DOI:10.1080/00224065.2010.11917824