Information, measure shifts and distribution diagnostics

Roger Bowden

No 33475, Working Paper Series from Victoria University of Wellington, School of Economics and Finance

Abstract: Reflexive shifting of a given distribution, using its own distribution function, can reveal information. The shifts are changes in measure accomplished via simple Radon-Nikodym derivatives. The separation of the resulting left and right unit shifted distributions reveals the binary entropy of location. Recombining the shifts via convex combinations yields information-based asymmetry and spread metrics as well as insight into latent structure. The resulting diagnostics are applicable even for long tail densities where distributional moments may not exist, and independently also of benchmarks such as the Gaussian.

Keywords: Asymmetry; Entropy bandwith; Locational entropy; Distribution Spread; Reflexive shifting; Unit distribution shifts (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:vuw:vuwecf:33475

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