This article demonstrates the utility of concentration functions in statistical data analysis, suggesting practical applications in visualizing probability measures.
Several notions of concentration function have been proposed in the statistical literature. Here we will refer to the definition by Cifarelli and Regazzini (1987), used for the comparison of probability measures in very general probability spaces. We will consider the concentration function in more restricted settings, typically those of interest to practitioners, that is, discrete or absolutely continuous (with respect to the Lebesgue measure) probability measures. We will show how a sophisticated mathematical tool can be used to provide graphs and indices that are easily interpreted by practitioners. Some examples will support this statement. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Exploratory Data Analysis Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization
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Fabrizio Ruggeri (2025) studied this question.
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