Czstotliwo

Czstotliwo is a theoretical construct used in time-series analysis to quantify the density of discrete events as they occur in time, especially for non-stationary processes. It is conceptually akin to the instantaneous rate or intensity function in stochastic modeling. For a counting process N(t), Czstotliwo at time t can be defined as C(t) = dN(t)/dt, or, more practically, as a finite-difference estimate C(t) ≈ [N(t+Δ) − N(t)]/Δ using a chosen window Δ. The unit is events per unit time, and C(t) may vary with time reflecting changing activity.

The term Czstotliwo is a coined form influenced by the Polish word częstotliwość, meaning frequency; its spelling with an altered prefix signals a stylized or specialized usage in certain texts and discussions. It is not a widely standardized measure across disciplines, and different authors may propose alternative definitions or estimation methods.

In practice, Czstotliwo can be estimated by moving-window counts, kernel smoothing, or model-based intensity estimation. It is related to, but distinct from, spectral quantities such as power spectra and from the autocorrelation function; it emphasizes time-domain activity rather than frequency components. Applications appear in neuroscience (spike trains), seismology (earthquake aftershock rates), telecommunications (traffic load), and ecology (event timing).

Limitations include sensitivity to window size and to counting noise, potential bias near data boundaries, and interpretive ambiguity when the underlying process includes multiple interacting rhythms.

See also: frequency; instantaneous frequency; intensity function; non-homogeneous Poisson process.