Dreifingarbreytingar

Dreifingarbreytingar is a term used in Icelandic statistics and related fields to describe changes in the distribution of a variable. It covers any alteration in the probability distribution, including shifts in location (mean), changes in scale (variance), and changes in shape (skewness and kurtosis), as well as more complex alterations such as mixing of distributions or changes in the entire functional form.

In practice, dreifingarbreytingar are analyzed by comparing distributions across time, groups, or conditions. Common approaches include nonparametric tests such as the Kolmogorov–Smirnov test, graphical methods, and model-based methods that allow for distributional changes, such as distribution regression, quantile regression, and generalized additive models for location, scale, and shape (GAMLSS).

Mathematically, if X has a distribution F, a dreifingarbreyting can occur through a transformation Y = g(X) or through changes in parameters of the distribution family F_theta. Decomposing observed differences into components attributable to shifts in the distribution of covariates vs. changes in the response distribution is a typical task in econometrics and social sciences.

Applications of dreifingarbreytingar include assessing the impact of policies on income or wealth distributions, tracking epidemiological trends in the distribution of age or severity, and evaluating risk in finance through changes in return distributions.

See also: Probability distribution; Transformation of random variables; Kolmogorov–Smirnov test; quantile regression; GAMLSS.