A hazard function is a statistical tool used to describe the instantaneous risk of an event occurring at a specific time, given that the event has not yet happened. It is commonly used in survival analysis to model the time until an event, such as failure of a machine or death of an organism. The hazard function helps researchers understand how the risk changes over time. In mathematical terms, the hazard function is often denoted as h(t), where t represents time. It can be derived from the survival function, which indicates the probability of surviving past a certain time. By analyzing the hazard function, researchers can identify patterns and factors that influence the timing of events.