Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing
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Date
Authors
Mac’Oduol, B.V. (Brenda)
Van Staden, Paul Jacobus
King, Robert A.R.
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor and Francis
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.
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Keywords
Cumulative distribution function (CDF), Two-piece, Half distributions, Quantile functions, L-moments, Asymmetric generalization, Symmetric univariate probability distribution, Quantile splicing
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Citation
Brenda V. Mac’Oduol, Paul J. van Staden & Robert A. R. King (2020): Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing, Communications in Statistics - Theory and Methods 49(18): 4413-4429, DOI: 10.1080/03610926.2019.1601219.