W-transforms: Uniformity-preserving transformations and induced dependence structures

Abstract

W-transforms are introduced as uniformity-preserving univariate transformations on the unit interval induced by distribution functions and piecewise strictly monotone functions, and their properties are investigated. When applied componentwise to random vectors with standard uniform univariate margins, W-transforms naturally serve as copula-to-copula transformations. Properties of the resulting W-transformed copulas, including their analytical form, density, measures of concordance, tail dependence and symmetries, are derived. A flexible parametric family of W-transforms is proposed as a special case to further enhance tractability. Illustrative examples highlight the introduced concepts, and improved dependence modelling is demonstrated in terms of a real-life dataset.