selviämisfunktio

A selviämisfunktio, often translated as survival function, is a fundamental concept in survival analysis, a branch of statistics used to analyze the expected duration of time until one or more events happen. The survival function, denoted as S(t), represents the probability that an individual or unit will survive beyond a specific time point t. Mathematically, it is defined as the complement of the cumulative distribution function (CDF), F(t), where F(t) is the probability of the event occurring at or before time t. Therefore, S(t) = P(T > t) = 1 - F(t), where T is a random variable representing the time until the event.

The survival function is always non-increasing, meaning that as time progresses, the probability of survival either stays the same or decreases. It starts at 1 (or 100%) at time t=0, as there's a certainty of survival at the very beginning. As time t increases, S(t) will eventually approach 0, indicating that the probability of survival over very long periods diminishes. Key characteristics of the survival function include its ability to describe the pattern of event occurrences over time, identify median survival times, and compare survival experiences between different groups. It is widely applied in fields such as medicine to study patient recovery or disease progression, engineering for reliability analysis of components, and demography for life expectancy studies.