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Asymmetric generalizations of symmetric univariate probability distributions obtained through quantile splicing

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

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.

Suggested 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, Taylor & Francis Journals, vol. 49(18), pages 4413-4429, September.
    • Handle: RePEc:taf:lstaxx:v:49:y:2020:i:18:p:4413-4429
    DOI: 10.1080/03610926.2019.1601219
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