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

作者：Critchley Frank; Jones M C^*

来源：Scandinavian Journal of Statistics, 2008, 35(3): 415-437.

DOI：10.1111/j.1467-9469.2008.00599.x

• density derivative
• density inverse
• kernel estimation
• Khintchine's theorem
• mode
• unimodal distribution

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.

• 出版日期2008-9