Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing

Brenda V. Mac’Oduol, Paul J. van Staden and Robert A. R. King

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 18, 4413-4429

Abstract: Balakrishnan et al. proposed a two-piece skew logistic distribution by making use of the cumulative distribution function (CDF) of half distributions as the building block, to give rise to an asymmetric family of two-piece distributions, through the inclusion of a single shape parameter. This paper proposes the construction of asymmetric families of two-piece distributions by making use of quantile functions of symmetric distributions as building blocks. This proposition will enable the derivation of a general formula for the L-moments of two-piece distributions. Examples will be presented, where the logistic, normal, Student’s t(2) and hyperbolic secant distributions are considered.

Date: 2020
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DOI: 10.1080/03610926.2019.1601219

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