An increasing variety of outcomes is being identified to have heavy tail distributions including income distributions financial returns insurance payouts reference links on the web etc. In probability theory heavy tailed distributions are probability distributions whose tails are not exponentially bounded.

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### There are three important subclasses of heavy tailed distributions.

**Heavy tail distribution**. 1 that is they have heavier tails than the exponential distribution. This means that regardless of the distribution for small values of therandom variable if the asymptotic shape of the distribution ishyperbolic it is heavy tailed 7. Heavy tail means that there is a larger probability of getting very large values.

A random variable xis said to have the weibull distribution with shape param. The distribution of city sizes rrgm11 gab16. Heavy tailed distributions htds ccdf decays slower than the exponential distribution ccdf complementary cumulative distribution function for heavy tailed distributions ccdf is slower by some power of x very large values possible 1 f x x.

So heavy tail distributions typically represent wild as opposed to mild randomness. The firm size distribution axt01 gab16 the distribution of returns on holding assets over short time horizons man63 rac03 and. In many applications it is the right tail of the distribution that is of interest but a distribution may have a heavy left tail or both tails may be heavy.

Heavy tailed distributions tend to have many outliers with very high values. In many applications it is the right tail of the distribution that is of interest but a distribution may have a heavy left tail or both tails may be heavy. In other words a distribution that is heavy tailed goes to zero slower than one with heavy tails.

There will be more bulk under the curve of the pdf. The fat tailed distributions the long tailed distributions and the subexponential distributions. A distribution is said to have a heavy tail if.

A heavy tailed distribution has a tail that s heavier than an exponential distribution bryson 1974. Heavy tailed distributions are of interest because they can be used to model processes which have a tendency to produce extreme outcomes. These heavy tails turn out to be important for our understanding of economic outcomes.

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