Shape measures based on the convex transform order

A. Arriaza (), A. Crescenzo, M. A. Sordo and A. Suárez-Llorens
Additional contact information
A. Arriaza: Universidad de Cádiz
A. Crescenzo: Università di Salerno
M. A. Sordo: Universidad de Cádiz
A. Suárez-Llorens: Universidad de Cádiz

Metrika: International Journal for Theoretical and Applied Statistics, 2019, vol. 82, issue 1, No 6, 99-124

Abstract: Abstract Three functional measures of the shape of univariate distributions are proposed which are consistent with respect to the convex transform order. The first two are weighted tail indices that characterize location-scale families of distributions, whilst the third is a skewness measure. Properties of the new measures are established for various classes of symmetric and asymmetric distributions, and the generalized Pareto distribution characterized in terms of them. Kernel density based estimation of the measures is also considered, and the use of the estimated functionals is illustrated in the analysis of two real data sets.

Keywords: Convex transform order; Kurtosis; Shape; Skewness; Stochastic order; Tail weight; Generalized Pareto distribution (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-018-0667-y

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