eventoccurrence

Event occurrence is a general concept used to describe the realization or happening of a defined event within a model or system. It denotes the moment or condition at which a specified outcome is observed or registered, depending on the framework being used.

In probability theory, an event A is a subset of the sample space. Its occurrence on a single trial means the observed outcome ω lies in A. The indicator I_A(ω) equals 1 if A occurs and 0 otherwise, and the probability of occurrence is P(A). Events can be independent, dependent, or conditional on other events, and combinations of events are described by unions, intersections, and complements.

In time-to-event or survival analysis, the focus is the time T until the occurrence of a particular event. The survival function S(t) = P(T > t) and the hazard function λ(t) describe the changing risk of occurrence over time, while censoring accounts for incomplete observation of T.

In stochastic processes such as the Poisson process, events occur randomly in time with a rate λ. Interarrival times are exponentially distributed, and the counting process N(t) records the number of occurrences up to time t. Properties like stationarity and independence simplify modeling of event occurrences.

In computer science, event occurrence refers to when an external or internal stimulus triggers an event in an event-driven system. An event loop dispatches handlers or callbacks in response to occurrences such as user input, messages, or timer signals.

In data collection and quality control, counting event occurrences over a time or space interval provides estimates of rate or intensity. The Poisson distribution or related models are commonly used for the probability of k occurrences in a fixed interval under assumptions of independence and a constant average rate.