Moment-Ratio Diagrams for Univariate Distributions

  • Erik Vargo
  • Raghu Pasupathy
  • Lawrence M. Leemis
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 247)


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.


Coefficient of variation Kurtosis Skewness 


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Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  • Erik Vargo
    • 1
  • Raghu Pasupathy
    • 2
  • Lawrence M. Leemis
    • 3
  1. 1.MITREMcLeanUSA
  2. 2.Purdue UniversityWest LafayetteUSA
  3. 3.The College of William and MaryWilliamsburgUSA

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