Under a Gaussian distribution extreme tail events become effectively impossible

Evidence

To understand why this is important, imagine that we have sampled the height of 10,000 randomly selected adults. We find out that most people are between five and six feet tall, that far fewer people are either seven feet or three feet tall, and that no one in our sample is outside that range. Knowing this, we can figure out the probability of any one person of a given size being close to the mean of the distribution. Under a normal distribution, a one-sigma deviation means that there is a 68 percent chance that person is close to the mean height. Two sigmas translates into a 95 percent chance of being close to the mean, and so on, out into the (very) thin tails, where no one is ever eight feet tall. As the numbers get bigger, the probability of encountering someone of such an extreme size gets exponentially smaller. The chance that someone will fall completely outside the sample becomes so unlikely that you can basically forget about it. — Mark Blyth, Austerity, 106

Categorization

• DEFINE: Walks through the bell-curve logic in concrete height terms, making sigma probabilities legible for the non-statistician reader.
• XREF: connects to: Levy distributions yield more stable estimates of extreme moves than variance-based methods — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 937; A single exponent alpha parametrizes a family spanning normal to wildly fatal-tailed distributions — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 479; Mainstream statistics training in the 1970s ignored Levy distributions — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 481 (+9 more)

Broader Connections

• Levy distributions yield more stable estimates of extreme moves than variance-based methods #expands (0.80) — Donald MacKenzie, An Engine, Not a Camera, 937
• A single exponent alpha parametrizes a family spanning normal to wildly fatal-tailed distributions #expands (0.80) — Donald MacKenzie, An Engine, Not a Camera, 479
• Statistical models cannot anticipate events outside their sampled historical range #expands (0.80) — Mark Blyth, Austerity, 112
• Claiming that correlated market crises are statistically impossible is plainly false #qualifies (0.80) — Mark Blyth, Austerity, 104
• The bell-curve shape of Gaussian distributions is what banks’ risk models assume #corroborates (0.75)
• More sampling of a rare risk gives false confidence right before catastrophe #complicates (0.75) — Mark Blyth, Austerity, 113
• Mainstream statistics training in the 1970s ignored Levy distributions #responds-to (0.72) — Donald MacKenzie, An Engine, Not a Camera, 481
• Levy distributions keep identical form across every timescale, making scale irrelevant #expands (0.72) — Donald MacKenzie, An Engine, Not a Camera, 492
• Probabilistic valuation methods migrated from actuarial science into financial markets via Gaussian risk models #responds-to (0.72) — Ève Chiapello, Financialisation of Valuation, 33
• The Levy distribution’s failure to survive time aggregation cooled academic interest in fat tails #responds-to (0.70) — Donald MacKenzie, An Engine, Not a Camera, 509