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http://dx.doi.org/10.7465/jkdi.2017.28.5.959

Bivariate skewness, kurtosis and surface plot  

Hong, Chong Sun (Department of Statistics, Sungkyunkwan University)
Sung, Jae Hyun (Department of Statistics, Sungkyunkwan University)
Publication Information
Journal of the Korean Data and Information Science Society / v.28, no.5, 2017 , pp. 959-970 More about this Journal
Abstract
In this study, we propose bivariate skewness and kurtosis statistics and suggest a surface plot that can visually implement bivariate data containing the correlation coefficient. The skewness statistic is expressed in the form of a paired real values because this represents the skewed directions and degrees of the bivariate random sample. The kurtosis has a positive value which can determine how thick the tail part of the data is compared to the bivariate normal distribution. Moreover, the surface plot implements bivariate data based on the quantile vectors. Skewness and kurtosis are obtained and surface plots are explored for various types of bivariate data. With these results, it has been found that the values of the skewness and kurtosis reflect the characteristics of the bivariate data implemented by the surface plots. Therefore, the skewness, kurtosis and surface plot proposed in this paper could be used as one of valuable descriptive statistical methods for analyzing bivariate distributions.
Keywords
Box plot; mahalanobis distance; mixture; quantile vector; surface plot;
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Times Cited By KSCI : 3  (Citation Analysis)
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