In practical risk assessment applications, the probabilistic component of risk is defined through the hazardous event frequency. However, unwanted scenarios are not usually caused by single events and their probabilities require a more detailed description that takes into account their nature and evolution over time. Here we introduce the hazard functions, both in the discrete and continuous domain, and the corresponding univariate theorems that relate the probabilistic component of risk to the cumulative distribution function, which is well known in reliability theory as the failure function or the lifetime distribution function. This approach is applied in the estimation of the risk of worst case scenario (worst case risk), which by this method is reduced to the probability assessment of extreme events occurrence.