viktbidrag

Viktbidrag is a term used in Swedish statistics and data analysis to describe how much a individual observation or component contributes to a weighted aggregate. The concept arises whenever weights are assigned to elements to reflect importance, frequency, reliability, or sampling design, and it helps to interpret the influence of each part on the overall result.

In a weighted sum, S = sum_i w_i x_i, the viktbidrag of observation i is the product w_i x_i. When considering a weighted mean, the relative viktbidrag is (w_i x_i) / sum_j w_j, which shows how much observation i contributes to the final average. For example, with x = [10, 20, 30] and weights w = [2, 3, 5], the weighted sum components are 20, 60, and 150; the total is 230, and the weighted mean is 230 / (2+3+5) = 23, with relative viktbidrag 20/10 = 2, 60/10 = 6, and 150/10 = 15 for the three observations.

Applications of viktbidrag include public statistics and policy analysis, where it helps to show how different groups or design strata contribute to a metric; econometrics and data science, where it aids interpretation of model outputs under weighting schemes; and actuarial contexts, where weights reflect sampling schemes or risk factors. Etymologically, it combines vikt (weight) and bidrag (contribution). Related concepts include weighted averages and sampling weights.