fordelesfordelt

Fordelesfordelt is a term used in statistics and economics to describe a situation in which a primary quantity is distributed across subgroups in a manner that itself induces a distribution over the subgroups. The term combines the Danish roots fordeles (to distribute) and fordelt (distributed).

In theoretical usage, fordelesfordelt can refer to hierarchical or compound distributions, where a total resource is allocated according to a first-stage distribution and, within each category, allocations follow secondary distributions. It is encountered in models of budget allocation, risk sharing, and ecological resource division, where the joint behavior of subgroups is of interest.

Formally, if a total amount T is fixed and allocated across k groups so that X = (X1, ..., Xk) denotes the allocations and the sum of Xi equals T, then the pattern may be described as fordelesfordelt when Xi are governed by a hierarchy of distributions, for example Xi given Yi with Yi distributed across groups and Xi conditional on Yi following Fi(Yi).

For example, a budget of 100 units divided among three departments might use a first-stage allocation of shares to departments, followed by secondary allocations within each department. The resulting structure of suballocations can be described as fordelesfordelt, reflecting the layered nature of the distribution.

See also: distribution theory, hierarchical models, Dirichlet distribution, resource allocation.

Because fordelesfordelt is not widely standardized, different sources may define it differently or use the term informally to describe related hierarchical or compound distributions.