Kumulierte

Kumulierte is a German adjective and past participle formed from kumulieren, meaning to accumulate or pile up. It denotes something that has been gathered, built up, or added over time. In technical writing and everyday language, kumulierte describes totals, aggregates, or results that emerge from successive additions. The form inflects for gender, number, and case, for example kumulierte Ergebnisse (plural) or der kumulierte Wert (singular, masculine).

In statistics and data analysis, kumulierte is widely used in expressions such as kumulierte Verteilungsfunktion and kumulative Häufigkeit. The kumulative Verteilungsfunktion, or cumulative distribution function (CDF), gives the probability that a random variable does not exceed a certain value. The kumulative Häufigkeit represents the total number or proportion of observations with values up to a given threshold, reflecting the accumulation of data points up to that point.

In finance and accounting, kumulierte Größen refer to quantities accumulated over time. Examples include kumulierte Rendite (cumulative return) and kumulierte Zinsen (accrued or accumulated interest). These measures emphasize the aggregate effect of returns or interest across multiple periods rather than single-period values.

Etymology and scope: kumulieren derives from the Latin cumulus (a heap) and entered German through scientific and mathematical usage in the 18th and 19th centuries. Today, kumulierte appears in a range of disciplines, from mathematics and statistics to economics, finance, and general data reporting, where the concept of accumulation and aggregation over time is central.