The next time someone asks when you think things might get back to normal, you might reply, like Flyvbjer, "I don't think we will see a regression to the mean because pandemics, like earthquakes and bankruptcies, don't follow the rules of Gaussian distribution." That'll stop the conversation right there.

We live under the assumption that most things in life follow a pattern of standard distribution. This is the basis for the idea of regression to the mean which is deeply ingrained in most of us. For that reason and others, we imagine things going *back to normal*. But not all events occur with standard distribution.

Size-distributions of pandemics, floods, wildfires, earthquakes, wars, and terrorist attacks, e.g., have no population mean, or the mean is ill defined due to infinite variance. In other words, mean and/or variance do not exist. Regression to the mean is a meaningless concept for such distributions, whereas what one might call "regression to the tail" is meaningful and consequential.

In disaster recovery, there can never be a return to the way things were [1]. Return to normal or *regression to the mean*, is *meaningless*. There are a few options; abandon ship (or house, or town, or country, or planet… is that an option??), build back better, or rebuild in some other way. If not better then what? If not back to normal, then what?

With *fat-tailed distribution*, there is no limit to the extremes, there is no standard distribution.

In other words, “no matter how extreme the most extreme event is, there will always be an event even more extreme than this.” This is true of pandemics, natural disasters, and other phenomena (see table 1).

**Table 1**

**Top 10 phenomena that are subject to the law of regression to the tail, ranked after fatness of tails. The higher on the list, the fatter the tail, and the larger and more frequent regressions to the tail will be. All phenomena have infinite variance. The table shows phenomena for which data were available.**

Earthquakes (intensity as Richter Scale maximum peak) | |

Cybercrime (financial loss) | |

Wars (number of battle deaths per capita of involved nations) | |

Pandemics (number of deaths) | |

IT procurement (percentage size of cost overrun) | |

Floods (volume of water) | |

Bankruptcies (percent of firms per year per industry) | |

Forest fires (size of area affected) | |

Olympic Games (percentage size of cost overrun) | |

Blackouts (number of customers affected) |

The connection between infectious disease outbreaks and climate change is a fascinating, scary, and beyond the scope of this little writeup. In addition to causal links they are intricately connected politically and socially.

A positive way to view covid-19 is to see it as a much-needed opportunity for humanity to exercise its skills in managing regression to the tail

Both natural disasters and pandemics are extreme events that do not follow standard distribution, meaning that future pandemics will occur, worse than the current one; and future climate events will occur, worse than the worst we’ve seen to this point. Both crises require a proactive and comprehensive approach to eliminate risks in order to end the crisis, unlike events that will of their own accord, *regress to the mean* (return to normal).

References

Bly J, Francescutti LH, Weiss D. Disaster Management: A State-of-the-Art Review. Natural Hazards-Impacts, Adjustments & Resilience. 2020 Nov 12.

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