Verteilungsbild

Verteilungsbild is a German term for the graphical representation of the distribution of a random variable or a data set. It provides a visual summary of how values are concentrated, spread, and structured, complementing numerical descriptors such as mean, median and variance. A Verteilungsbild can be empirical, based on observed data, or theoretical, illustrating a specified probability distribution.

Common forms include histograms, which show frequencies per value or bin; density plots, which display the probability density function or its smoothed version via kernel density estimation; and cumulative plots that depict the cumulative distribution function or the empirical distribution function. Box plots and Q-Q plots can also contribute to the Verteilungsbild by illustrating spread, skewness and deviations from a reference distribution.

Construction: for empirical data, one typically builds a histogram or an empirical distribution function, or fits a model and plots its PDF or CDF. For theoretical distributions, plots show the corresponding density and accumulation. The Verteilungsbild thus visualizes either observed patterns or expected behavior under a specified model.

Interpretation: the shape reveals modality (unimodal, bimodal), skewness (left or right) and tail behavior; outliers may appear as isolated points or distant observations; comparisons of Verteilungsbilder across groups help assess differences in distributions.

Relation to other concepts: while the Verteilungsbild is a visualization, the underlying distribution is described by a Verteilungsfunktion (CDF) or Dichte (PDF). Inference and hypothesis testing often rely on such visual assessments in combination with quantitative measures.

Limitations: bin width, scaling and sampling variability affect interpretation; therefore, visual inspection should be complemented by numerical summaries and formal tests.