Randgrößen

Randgrößen is a German term used in several disciplines to denote quantities that describe the boundary, margin, or edge of a system. The common idea is that Randgrößen summarize information located at the border and are often needed to complete or constrain analyses. In mathematics and applied sciences Randgrößen frequently appear as boundary values.

In boundary-value problems for partial differential equations, Randgrößen are the data specified on the boundary of the domain. They determine the solution inside the domain through conditions such as Dirichlet data (values of the unknown function on the boundary), Neumann data (values of the normal derivative on the boundary), or Robin data (a linear combination prescribed on the boundary). These Randgrößen are essential for the well-posedness of the problem and influence the interior solution.

In statistics and probability, Randgrößen commonly refer to marginal quantities of a joint distribution. For example, in a joint distribution of (X, Y), the Randgröße for X is its marginal distribution, obtained by summing (or integrating) over Y: P_X(x) = sum_y P_{X,Y}(x, y). Similarly, P_Y(y) is the margin for Y. In contingency tables, Randgrößen are the row and column totals, or marginal distributions, that summarize counts along the borders of the table.

Etymologically, Rand means boundary or edge and Größe means quantity or size. Related concepts include boundary conditions, margins, and marginal distributions.