Fat Tails
Notes and Code for fat-tailed statistics. Inspired by Nassim Taleb's Technical Incerto.
Table of Contents
Notebooks
See the notebooks/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
External Resources
Technical Incerto Book One:
- Free PDF: researchers.one, arxiv.org
- Errata: fooledbyrandomness.com
More Links:
- Incerto Reading Club: Website
StatisticalConsequencesOfFatTails: Code and Links collected by Marcos Carreira- Anthony Voto: Diagnosing the SP500 Twitter thread, GitHub Code
Other Notes
Contact ✉
How to reach me:
@MFergalon Twitter
Contributors
Special thanks to:
- Daniel Reti: github.com/drettt
Python Package
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 datapointfattails.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 data
0 0.75
1 0.50
2 0.25
Name: survival_probability, dtype: float64
Derivations
Roughwork: