A hyperbolic distribution is a type of probability distribution that is commonly used to model the behavior of complex systems or processes. This distribution is characterized by its heavy tails, which means that it has a higher probability of extreme values than other distributions.

One example of a hyperbolic distribution is the Pareto distribution, which is often used to model the distribution of wealth in a society. In this distribution, the probability of having a high wealth is much higher than the probability of having a low wealth. This is because the distribution has a long right tail, which means that there is a higher probability of having extreme wealth values.

Another example of a hyperbolic distribution is the power law distribution, which is commonly used to model the distribution of sizes in a population. In this distribution, the probability of having a large size is much higher than the probability of having a small size. This is because the distribution has a long right tail, which means that there is a higher probability of having extreme size values.

Overall, hyperbolic distributions are useful for modeling complex systems or processes that exhibit extreme behavior. They are characterized by their heavy tails, which make them more likely to have extreme values than other distributions.