Some Notes on Bivariate Lower Semilinear Copulas

We revisit the class of bivariate lower semilinear copulas (LSL) as introduced by Durante et al. in 2008 (see [2]), view LSL copulas from the Markov kernel perspective, and use the kernel to derive a simple formula for the singular mass of arbitrary LSL copulas. Complementing these results we derive simple formulas for Kendall’s \(\tau \) and Spearman’s \(\rho \) and study monotonicity/ordering properties like positive quadrant dependence (PQD), left tail dependence (LTD) and stochastic increasingness (SI).