Generic Measures of Distributional Peakedness, Locational Differences and Modally Focused Kurtosis and Relative Variation Coefficients: Tools for Mode-based Analyses

Gordon Anderson

Working Papers from University of Toronto, Department of Economics

Abstract: More often than not in summarizing the level of and variation in outcomes, the Mean or Median are the focus, however, as the most frequently observed outcome, there are good reasons for using the Mode in that role. Its pertinence for that purpose hinges on the extent to which it differs from the other centrality statistics and its prominence or “Peakedness†in the distributional density profile. Peakedness is usually calibrated using Pearsons Kurtosis quotient however, that measure has been shown to be more about the fatness of a distribution’s tails rather than its Peakedness. Here, generic probabilistically based measures of the extent to which location points differ and the extent to which distributions are peaked, suitable for any discrete or continuous potentially multidimensional data environment are proposed together with modally focused analogues of Pearsons Relative Variation and Kurtosis measures, appropriate for distributions which are not symmetric unimodal. Applications in five very different distributional environments demonstrate the usefulness and general applicability of these new measures.

Keywords: Skewness; Kurtosis; Peakedness. (search for similar items in EconPapers)
JEL-codes: C1 D0 E0 G0 I0 (search for similar items in EconPapers)
Pages: Unknown pages
Date: 2026-01-09
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