TypeFrequenz

TypeFrequenz is a metric used to quantify the rate at which a particular type or category appears within a data sequence. It is used across disciplines such as linguistics, data mining, and information theory to summarize the distribution of discrete types in time or space.

Formal definition: Consider a data stream of events labeled with discrete types. The TypeFrequenz of type t over a window W with N events is f_W(t) = n_W(t) / N, where n_W(t) is the count of events of type t in W. In continuous time, the asymptotic rate f(t) = lim_{T→∞} n_T(t)/T gives the long-run arrival rate of type t. TypeFrequenz thus normalizes counts by window length rather than using absolute counts, enabling comparison across samples of different sizes.

Computation and methods: It can be estimated with fixed windows, sliding windows, or online estimators such as exponential smoothing. It is used to compare type distributions, detect shifts, model language usage, analyze network traffic, sensor streams, or user behavior.

Examples and caveats: In a text corpus, the TypeFrequenz of a common function word might be high, e.g., 0.07 of tokens in a large English corpus. However, TypeFrequenz depends on the chosen time scale, labeling granularity, and sampling method; different definitions of a "type" yield different results.

See also: Frequency, probability distribution, Zipf's law, event rate.