tailindex
Tailindex is a parameter that quantifies how heavy the tails of a probability distribution are. In the language of regular variation, a distribution has tailindex alpha > 0 if its survival function satisfies P(X > x) ~ x^(-alpha) L(x) as x grows large, where L is a slowly varying function. A larger tailindex corresponds to a lighter tail; smaller values indicate heavier tails. If alpha > k, moments up to order k exist; if alpha ≤ k, the k-th moment is infinite. The Pareto distribution is a canonical example whose tailindex equals its shape parameter alpha.
In extreme value theory, the tailindex links to the behavior of extremes. Distributions with regularly varying
Estimation methods focus on the tail observations. The Hill estimator uses the largest order statistics to
Applications of tailindex span finance, insurance, environmental science, and risk assessment, where understanding tail behavior informs
See also: heavy-tailed distributions, regularly varying functions, Pareto distribution, Hill estimator, extreme value theory.