# Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications

arXiv: https://arxiv.org/abs/2001.10488 · HTML: https://mlsanity.com/paper/2001.10488/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jan 2020.

## Built on by (most cited first, 16 of 16)

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- [Safe Pruning LoRA: Robust Distance-Guided Pruning for Safety Alignment in Adaptation of LLMs](https://mlsanity.com/paper/2506.18931/) (2025)
- [Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confounding](https://mlsanity.com/paper/2306.09520/) (2023)
- [Multidimensional Knowledge Graph Embeddings for International Trade Flow Analysis](https://mlsanity.com/paper/2410.19835/) (2024)
- [Two-parameter superposable S-curves](https://mlsanity.com/paper/2504.19488/) (2025)
- [Interpreting Emergent Extreme Events in Multi-Agent Systems](https://mlsanity.com/paper/2601.20538/) (2026)
- [Quantified Sleep: Machine learning techniques for observational n-of-1 studies](https://mlsanity.com/paper/2105.06811/) (2021)
- [Modularity Trumps Invariance for Compositional Robustness](https://mlsanity.com/paper/2306.09005/) (2023)
- [Streaming Bayesian Modeling for predicting Fat-Tailed Customer Lifetime Value](https://mlsanity.com/paper/2312.00373/) (2023)
- [Stochastic Processes with Modified Lognormal Distribution Featuring Flexible Upper Tail](https://mlsanity.com/paper/2505.14713/) (2025)
- [ERRORQUAKE: Heavy-Tailed Error Severity Distributions in Open-Weight Large Language Models](https://mlsanity.com/paper/2606.05170/) (2026)
- [A Policy Algebra for Trust-Preserving Agentic AI Execution](https://mlsanity.com/paper/2608.16402/) (2026)

## Abstract (arXiv)

(The third edition corrects minor typos and adds 3 chapters synthesized from published papers plus an appendix on maximum entropy distributions.) The monograph investigates the misapplication of conventional statistical techniques to fat tailed distributions and looks for remedies, when possible. Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress". Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under of the "laws of the medium numbers" --which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: + The sample mean is rarely in line with the population mean, with effect on "naive empiricism", but can be sometimes be estimated via parametric methods. + The "empirical distribution" is rarely empirical. + Parameter uncertainty has compounding effects on statistical metrics. + Dimension reduction (principal components) fails. + Inequality estimators (GINI or quantile contributions) are not additive and produce wrong results. + Many "biases" found in psychology become entirely rational under more sophisticated probability distributions + Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.