Moment-ratio diagrams for univariate distributions. Vargo, E., Pasupathy, R., & Leemis, L. Journal of Quality Technology, 42(3):276–286, 2010. Paper abstract bibtex 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 moments can assume; and (3) they can be used to create a short list of potential probability models based on a data set; (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.
@article{2010varpaslee,
author = {E. Vargo and R. Pasupathy and L. Leemis},
title = {Moment-ratio diagrams for univariate distributions},
journal = {Journal of Quality Technology},
year = {2010},
volume = {42},
number = {3},
pages = {276--286},
doi = {},
url = {http://web.ics.purdue.edu/~pasupath/PAPERS/2010varpasleeCOLOR.pdf},
keywords = {moment-ratio diagrams},
abstract = {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 moments can assume; and (3) they can be used to create a short list of potential probability models based on a data set; (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.}}
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