Survival Analysis

Survival analysis is a branch of statistics that focuses on the study of time-to-event data, often referred to as survival times. This type of data is widely used in various fields, such as the time until failure of mechanical systems, the time until death of patients in clinical trials, and the duration of unemployment in populations. The primary objectives of survival analysis are to estimate the survival function and the hazard function, where the density function $f$ and the cumulative distribution function $F$ determine the survival function $S = 1 - F$ and the hazard function $\lambda = f / S$. Survival analysis has significant applications in predicting and understanding the temporal patterns of events.