A unified view on skewed distributions arising from selections

Reinaldo B. Arellano-Valle*, Márcia D. Branco, Marc Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

141 Scopus citations

Abstract

Parametric families of multivariate nonnormal distributions have received considerable attention in the past few decades. The authors propose a new definition of a selection distribution that encompasses many existing families of multivariate skewed distributions. Their work is motivated by examples that involve various forms of selection mechanisms and lead to skewed distributions. They give the main properties of selection distributions and show how various families of multivariate skewed distributions, such as the skew-normal and skew-elliptical distributions, arise as special cases. The authors further introduce several methods of constructing selection distributions based on linear and nonlinear selection mechanisms.

Original languageEnglish (US)
Pages (from-to)581-601
Number of pages21
JournalCanadian Journal of Statistics
Volume34
Issue number4
DOIs
StatePublished - Jan 1 2006

Keywords

  • Kurtosis
  • Multimodal distribution
  • Multivariate distribution
  • Nonnormal distribution
  • Selection mechanism
  • Skew-symmetric distribution
  • Skewness
  • Transformation

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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