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Moment-Ratio Diagrams for Univariate Distributions

In: Computational Probability Applications

Author

Listed:
  • Erik Vargo

    (MITRE)

  • Raghu Pasupathy

    (Purdue University)

  • Lawrence M. Leemis

    (The College of William and Mary)

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.

Suggested Citation

  • Erik Vargo & Raghu Pasupathy & Lawrence M. Leemis, 2017. "Moment-Ratio Diagrams for Univariate Distributions," International Series in Operations Research & Management Science, in: Andrew G. Glen & Lawrence M. Leemis (ed.), Computational Probability Applications, chapter 12, pages 149-164, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-43317-2_12
    DOI: 10.1007/978-3-319-43317-2_12
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    Cited by:

    1. Karagiorgis, Ariston & Drakos, Konstantinos, 2022. "The Skewness-Kurtosis plane for non-Gaussian systems: The case of hedge fund returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).

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