What Are Fat Tails? In statistics, fat tails describe a feature of some probability distributions where extreme events (very high or very low values) are more likely than they would be in a normal (bell-curve) distribution. Normal Distribution vs Fat-Tailed Distribution A normal distribution has thin tails: the chance of an event far from the mean (like 5 or more standard deviations) is extremely small. A fat-tailed distribution (like the Pareto, Cauchy, or Student’s t-distribution) has fatter t