Asymmetry and gradient asymmetry functions: density-based skewness and kurtosis

Critchley, Frank and Jones, M. C. (2008). Asymmetry and gradient asymmetry functions: density-based skewness and kurtosis. Scandinavian Journal of Statistics, 35(3) pp. 415–437.

DOI: https://doi.org/10.1111/j.1467-9469.2008.00599.x

Abstract

Functional measures of skewness and kurtosis, called asymmetry and gradient asymmetry functions, are described for continuous univariate unimodal distributions. They are defined and interpreted directly in terms of the density function and its derivative. Asymmetry is defined by comparing distances from points of equal density to the mode. Gradient asymmetry is defined, in novel fashion, as asymmetry of an appropriate function of the density derivative. Properties and illustrations of asymmetry and gradient asymmetry functions are presented. Estimation of them is considered and illustrated with an example. Scalar summary skewness and kurtosis measures associated with asymmetry and gradient asymmetry functions are discussed.

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About

• Item ORO ID
• 15742
• Item Type
• Journal Item
• ISSN
• 0303-6898
• Keywords
• density derivative; density inverse; kernel estimation; Khintchine's theorem; mode; unimodal distribution
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Colin Smith