Definition:Weight Function

This page is about weight function in the context of statistics. For other uses, see weight.

Definition

A weight function on a set $S$ is a mapping from $S$ to the real numbers:

$w: S \to \R$

It is common for the requirements of a specific application under discussion for the codomain of $w$ to be restricted to the positive reals:

$w: S \to \R_{\ge 0}$

The thing that determines whether a given mapping is a weight function depends more on how it is used.

Also see

• Definition:Normalized Weight Function
• Definition:Extended Weight Function

• Definition:Weighted Mean

• Definition:Weighted Graph, the application of a weight function to the edges of a graph.