then the distribution is said to have a fat tail if formula_2 is small. For instance, if formula_3, the variance and the skewness of the tail is mathematically undefined (a special property of the power-law distribution), and hence larger than any normal or exponential distribution. For values of formula_4, the claim of a fat tail is more ambiguous, because in this parameter range, the variance, skewness, and kurtosis can be finite, depending on the precise value of formula_4, and thus potentially smaller than a high-variance normal or exponential tail. This ambiguity often leads to disagreements about precisely what is or is not a fat-tailed distribution. For formula_6, the formula_7 moment is infinite, so for every power law distribution, some moments are undefined.