On a class of random distortions based on hazard-operator families

Motivated by case studies focusing on a random replacement model and a catastrophe-based failure model, in this paper we propose a class of random distortions obtained by acting on the baseline cumulative hazard through a family of random hazard operators. We investigate a semigroup property for such operator family and show how it is inherited by the induced distortions. We then focus on the associated random quantiles. Finally, we address order-preserving results for distorted lifetimes under three comparison schemes: (i) fixed distortions and varying baseline distribution functions, (ii) fixed baseline and ordered distortions, and (iii) simultaneous variations in both baselines and distortions.