ما معنى Heavy-tailed distribution, tail index؟

A distribution is heavy-tailed (in the Pareto sense) if $\P(X > x) = x^{-\alpha}L(x)$ for a slowly varying $L$ ($L(tx)/L(x) \to 1$ as $x \to \infty$ for every $t > 0$). The exponent $\alpha > 0$ is its tail index.