Mandelbrotian (Scalable) Variations
Gaussian bell curve distributions have probabilities that drop rapidly away from the mean, whereas Mandelbrotian (scalable) variations lack this restriction, allowing for extreme events.
THE IDEA
Remember this: the Gaussian–bell curve variations face a headwind that makes probabilities drop at a faster and faster rate as you move away from the mean, while “scalables,” or Mandelbrotian variations, do not have such a restriction. That’s pretty much most of what you need to know.
When to use it
Risk management in finance: Gaussian models underestimate tail risk, so Mandelbrotian distributions are used for value-at-risk calculations.
Analysis of city sizes, firm sizes, or website traffic often follows power laws, requiring scalable models.
Scientific experiment design: recognizing measurements might come from fat-tailed distributions to avoid underestimating outlier probabilities.
Insurance pricing: earthquakes, pandemics, and other rare events often follow Mandelbrotian patterns.
FROM THEORY TO EVERYDAY LIFE
In practice
Human Height vs. Wealth
Human height follows a Gaussian distribution, making extreme heights extremely rare. In contrast, wealth distribution follows a Mandelbrotian (power-law) distribution where extreme wealth is much more common than a Gaussian would predict.
A MOMENT TO REFLECT
Put it to work.
What real-world phenomena might follow scalable (Mandelbrotian) distributions rather than Gaussian?
How does assuming a Gaussian distribution affect risk assessment in finance or insurance?
Why is it problematic to use Gaussian models for systems that can produce extreme outliers?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Black Swan The Impact of the Highly Improbable With a new section On Robustness and Fragility (Nassim Nicholas Taleb)