Stable distribution

Common card · No. 355028

In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, α {\displaystyle \alpha } (see panel). Stable distributions have 0 < α ≤ 2 {\displaystyle 0<\alpha \leq 2} , with the upper bound corresponding to the normal distribution, and approaches the Dirac delta function in the limit as α → 0 {\displaystyle \alpha \rightarrow 0} . The distributions...

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