Tailweight with respect to the mode for unimodal distributions
type: Item
instance of: scholarly article
title: Tailweight with respect to the mode for unimodal distributions
zbMATH Open document ID: 0857.62006
DOI: 10.1016/0167-7152(95)00147-6
author: Anne-Laure Fougeres
author: Jean Avérous
author: Michel Meste
published in: Statistics \& Probability Letters
publication date: 1996-11-25T00:00:00Z
review text: Location, scale, skewness and tailweight are important concepts for the description of a probability distribution. The study of tails for skewed distributions presents a particular aspect for unimodal distributions: when we consider the graph of the probability density function, the mode seems to be an appealing centre. An analogous approach to the quantile-based description of \(F\) is envisaged; it takes the mode as reference and makes use of \(A_F\) and \(Q_F\) as location and dispersion functional parameters. The mode, as location parameter, does not preserve the stochastic ordering. However, its interpretation makes it more rational in certain circumstances than mean or median. So, a description with respect to the mode of a distribution would be welcomed. Basic definitions and notations are given in Section 2. Section 3 then deals with the concept of location with respect to the mode by making use of the modal central interval and its midpoint. A way to approach distributions in the mode-sense, using already known notions in the median-sense, is suggested. Section 4 concerns tailweight orderings and skewness. A location- and scale-free tailweight ordering is introduced to compare tail with respect to the mode, without assuming symmetry. Finally, mode-based concepts of qualitative aspects of skewness are considered.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E99
zbMATH DE Number: 926965
zbMATH Keywords: Levy concentration function
zbMATH Keywords: spread
zbMATH Keywords: unimodular distributions
zbMATH Keywords: location
zbMATH Keywords: mode
zbMATH Keywords: modal central interval
zbMATH Keywords: tailweight orderings
zbMATH Keywords: skewness
MaRDI profile type: Publication
full work available at URL: 0167-7152(95)00147-6
OpenAlex ID: W2093973165
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description: scientific article; zbMATH DE number 926965