Lévy Stable Distributions — Generalized Central Limit Theorem

Stability α: Skewness β: Sum n: Resample α=1.5

Lévy stable distributions S(α,β,γ,δ) are attractors for sums of i.i.d. heavy-tailed random variables (GCLT). The stability index α∈(0,2] controls tail weight: α=2 recovers the Gaussian, α=1 gives the Cauchy distribution. For α<2, variance is infinite.