stapeldiagram

Stapeldiagram, in Dutch, refers to a step diagram: a graphical representation where the dependent variable remains constant over an interval and changes value in discrete jumps at specific points. The resulting figure has a staircase-like appearance, with horizontal segments connected by vertical jumps. This form is used in various fields to illustrate piecewise-constant behavior or cumulative quantities.

Types and construction

A stapeldiagram can depict a step function, where the value is constant between successive points and jumps at threshold positions. Steps can be left-continuous or right-continuous, depending on how the jump points are aligned with the intervals. To construct one, organize the data or function values, determine the jump locations, draw horizontal lines at each constant value, and connect them with vertical lines at the transition points. The diagram can be oriented horizontally or vertically.

Applications

Stapeldiagrammen are common in mathematics and statistics for visualizing step functions and empirical distribution-related concepts. They are also used in data visualization to represent time series or event-driven data where measurements occur at discrete times and remain constant between events. In signal processing and numerical methods, they can illustrate piecewise-constant signals or approximations.

Relation to other concepts

Related ideas include the staircase plot and the general concept of a step function. The empirical distribution function of a sample, for example, is a classic step-like visualization. While the term may appear in different domains, the core idea remains the same: a graphical representation that emphasizes discrete levels and abrupt changes rather than smooth variation.

See also

Step function, staircase plot, empirical distribution function, time series.