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July 4, 2026PLOS complex systems.Open Access

Probability-turbulence divergence: A tunable allotaxonometric instrument for comparing heavy-tailed type-probability distributions

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Authors

PDPeter Sheridan DoddsJMJoshua R. MinotMAMichael V. Arnold

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Overview

Randomized trial explores a new method to compare type-probability distributions across complex systems, suggesting a need for better analysis tools.

Key Points

  • This research aims to introduce a new instrument, probability-turbulence divergence (PTD), for comparing type-probability distributions across systems.
  • Introduced probability-turbulence divergence modeled after rank-turbulence divergence.
  • Developed allotaxonographs to visualize probability turbulence and adjust for zero probabilities.
  • Examined examples from literature, social media, and ecology.
  • Probability-turbulence divergence enhances sensitivity to changes in type probabilities.
  • Showed the ability to generalize existing distance measures including L q norms and the Hellinger distance.
  • Explored tuning PTD to accommodate various scales of divergence in type probabilities, indicating distinct comparisons.

Cite This Study

Dodds et al. (2026) studied this question.

synapsesocial.com/papers/6a48a57289561a0c2d78e2d8https://doi.org/10.1371/journal.pcsy.0000077
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