Critchley, Frank and Jones, M. C.
(2008).
*Scandinavian Journal of Statistics*, 35(3) pp. 415–437.

DOI (Digital Object Identifier) Link: | http://doi.org/10.1111/j.1467-9469.2008.00599.x |
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## 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.

Item Type: | Journal Article |
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ISSN: | 0303-6898 |

Keywords: | density derivative; density inverse; kernel estimation; Khintchine's theorem; mode; unimodal distribution |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 15742 |

Depositing User: | Colin Smith |

Date Deposited: | 14 Apr 2009 15:12 |

Last Modified: | 15 Jan 2016 11:10 |

URI: | http://oro.open.ac.uk/id/eprint/15742 |

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