In practice, people almost never actually observe true 10-sigma events in real Gaussian processes. When someone claims a "10-sigma event" has occurred (especially in finance), it usually means one of these:
The model/assumption is wrong — Real-world data (stock returns, market crashes, etc.) usually has fat tails (higher kurtosis), meaning extreme events are far more common than a normal distribution predicts. Nassim Taleb's famous line captures this perfectly:
"When someone tells you it was a 10 sigma event, meaning it is 10 standard deviations and it is Gaussian; unless the information came from God, you can reject the Gaussian distribution for that domain."
It's a rhetorical way to say "this should have been statistically impossible" — used to emphasize how shocking/unexpected something was.
