The Cumulative Hazard Function is a statistical tool used in survival analysis to quantify the risk of an event occurring over time. It represents the accumulated hazard, or risk, of failure or death up to a certain time point. This function helps researchers understand how the likelihood of an event changes as time progresses. In mathematical terms, the Cumulative Hazard Function is the integral of the hazard function, which describes the instantaneous risk at any given moment. It is often used in fields like medicine, engineering, and finance to model time-to-event data and assess the effectiveness of treatments or interventions.