What are hazard theories?

Hazard theories are mathematical models used to describe the time until an event occurs, often in contexts like survival analysis, reliability engineering, and risk assessment. They focus on the "hazard rate," which is the instantaneous risk of an event happening at a particular time, given that it has not occurred yet. These theories help in understanding and predicting failures or events over time, taking into account various influencing factors. Common applications include medical research, engineering, and finance, where understanding the timing of events is crucial.