A probabilistic view on semilinear copulas

Abstract This article advances the theory on multivariate upper semilinear copulas. Probabilistic features of this class are discussed and three subclasses are investigated in detail. The first subclass consists of upper semilinear copulas whose survival copulas are generalised Marshall–Olkin copulas. The second subclass is defined in that they possess identical multivariate diagonals. The third subclass is a family of extendible upper semilinear copulas. Stochastic models and analytical characterisation theorems are derived for each of these subclasses.