incidences

Incidence is a term used across disciplines to denote the occurrence, rate, or frequency of something happening within a defined context. The plural form incidences is used when referring to multiple distinct occurrences or categories, though many technical uses treat incidence as a singular, uncountable statistic.

In epidemiology and public health, incidence refers to the number of new cases of a condition that develop in a defined population during a specific time period. It is often expressed as a cumulative incidence (proportion of the population developing the condition over the period) or as an incidence rate (incidence density), published per person-time units. Example: 500 new cases among 100,000 people over one year yields a cumulative incidence of 0.5% or 500 per 100,000 person-years, depending on the measurement.

In mathematics and geometry, incidence describes the relationship between objects, notably points and lines, where a point is said to be incident with a line if it lies on that line. This concept generalizes to incidence structures used in combinatorics and finite geometry.

In optics, incidence refers to the angle at which a ray or wavefront meets a surface, measured relative to the surface normal. The law of reflection and Snell's law of refraction depend on the incidence.

Other uses appear in linguistics, information science, and risk assessment, where incidences denote occurrences of events or conditions. The term is often clarified by specifying the population, time frame, and the exact definition of an occurrence.