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Information, measure shifts and distribution diagnostics

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  • Bowden, Roger

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.

Suggested Citation

  • Bowden, Roger, 2026. "Information, measure shifts and distribution diagnostics," Working Paper Series 33475, Victoria University of Wellington, School of Economics and Finance.
    • Handle: RePEc:vuw:vuwecf:33475
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    File URL: https://ir.wgtn.ac.nz/handle/123456789/33475
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