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Notes and Code for fat-tailed statistics. Inspired by Nassim Taleb's Technical Incerto.

• 1. Blog
• 2. Python Notebooks
• 3. External Resources
• Other

Seefattails/blog/

• 2023-10: I am drafting some articles about Entropy as used in information theory.

See thenotebooks/README.md for more detail.

My favourite notebooks so far:

• Central Limit Theorem: How the sum of Uniform values is Gaussian
• S&P500: How geometric average return is impossible
• GameStop: January 2021 was not an outlier if you assume Power Law tails.
• Tail Alpha: How to estimate the mean of a power law

Technical Incerto Book One:

• Free PDF:researchers.one,arxiv.org
• Errata:fooledbyrandomness.com

More Links:

• Uncertainty Reading Club:Website
• Code and Links collected by Marcos Carreira:StatisticalConsequencesOfFatTails
• Anthony Voto: Diagnosing the SP500Twitter thread,GitHub Code

How to reach me:

• @MFergal onTwitter

Special thanks to:

• Daniel Reti:github.com/drettt

I started this project as a Python Package. Since then I shifted focus to python notebooks instead. Below are some notes about the packaged code and functions.

Quick Access:

• fattails.mad(): Calculates mean absolute deviation.
• fattails.plot_MS_moments(): Plots the cumulative max/sum ratio of moments 1 to 4.

Other:

• fattails.metrics.get_survival_probability(): Calculate survival probabilities for a given dataset.
• fattails.metrics.calculate_moments(): Generate dataframe with the chosen moments for each datapoint
• fattails.metrics.max_over_sum(): Calculate the cumulative max/sum ratio

Example:

$ pip install fattails$ python>>> import fattails>>>>>>>>> fattails.mad([1,2,3]) # Calculate Mean Absolute Deviation of [1,2,3]0.6666666666666666>>>>>>>>> fattails.metrics.get_survival_probability([1,2,3]) # Get survival probability for each value in your data0    0.751    0.502    0.25Name: survival_probability, dtype: float64

Roughwork:

• How much data do I need?