The Cox model plays the most prominent role in analyzing time-to-event data, primarily because of its robustness against the distributional assumption on survival time. However, the baseline hazard function of the Cox model is regarded as a nuisance parameter, which is often of fundamental interest in medical research. Moreover, the appealing features of the Cox model are not carried over in joint modeling of time-to-event and longitudinal data. We propose a parametric proportional hazards model, which is parsimonious and flexible in the sense that it accommodates all four standard shapes of the hazard function (increasing, decreasing, unimodal and bathtub shape) at the small cost of estimating only three distributional parameters. We consider the application of the proposed model in recurrent event data and joint modeling setups. A simulation study and real data examples reveal that the proposed model can be valuable in adequately describing different types of time-to-event data.