Vgemiddeld

Vgemiddeld is a statistical measure used to summarize a set of observations by weighting each value according to its volatility or uncertainty. The term is used in Dutch-language statistical and data-science discussions to denote a volatility-adjusted average technique; it is analogous to inverse-variance weighting in meta-analysis, but applied to a general data series. In practice, Vgemiddeld helps to reduce the influence of observations that carry higher uncertainty.

Formally, suppose you have observations x_i with corresponding volatility proxies V_i (for example standard deviations σ_i). The Vgemiddeld is defined as a weighted mean: Vgemiddeld = (sum_i w_i x_i) / (sum_i w_i), where the weights w_i are chosen as w_i = 1 / V_i^2 (or, more generally, a function of V_i that reflects the uncertainty associated with x_i). If all V_i are equal, Vgemiddeld reduces to the ordinary arithmetic mean. The choice of the volatility proxy V_i determines how strongly uncertain observations influence the result.

Computation typically involves three steps: determine a suitable volatility proxy for each observation, compute the corresponding weights, and calculate the weighted average. This approach yields a central tendency estimate that is more robust to heterogeneity in uncertainty across observations, compared with the simple mean. It is conceptually related to inverse-variance weighting used in combining estimates from different sources, and is applied in fields where measurements have varying reliability, such as finance, engineering, and environmental science.

Limitations include the need for reliable volatility estimates, potential sensitivity to misspecified uncertainty models, and reduced robustness to outliers. See also weighted average, inverse-variance weighting, and uncertainty weighting.