Hyperbolic Distributions
- Distributions with heavy tails that assign relatively high probability to extreme values.
- Often used to model complex systems or processes prone to extreme outcomes.
- Common examples include the Pareto distribution and the power law distribution.
Definition
Section titled “Definition”A hyperbolic distribution is a type of probability distribution characterized by its heavy tails, meaning it assigns a higher probability to extreme values than many other distributions.
Explanation
Section titled “Explanation”Hyperbolic distributions are used to describe behaviors in complex systems or processes where extreme values occur more frequently than would be predicted by distributions without heavy tails. The heavy-tail property implies a long right tail in the distribution, producing a comparatively higher likelihood of very large observations.
Examples
Section titled “Examples”Pareto distribution
Section titled “Pareto distribution”The Pareto distribution 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 because the distribution has a long right tail, which implies a higher probability of extreme wealth values.
Power law distribution
Section titled “Power law distribution”The power law distribution 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 because the distribution has a long right tail, which implies a higher probability of extreme size values.
Use cases
Section titled “Use cases”Hyperbolic distributions are useful for modeling complex systems or processes that exhibit extreme behavior.
Related terms
Section titled “Related terms”- Pareto distribution
- Power law distribution