Theory of probability distributions | Stability (probability)

Stability (probability)

In probability theory, the stability of a random variable is the property that a linear combination of two independent copies of the variable has the same distribution, up to location and scale parameters. The distributions of random variables having this property are said to be "stable distributions". Results available in probability theory show that all possible distributions having this property are members of a four-parameter family of distributions. The article on the stable distribution describes this family together with some of the properties of these distributions. The importance in probability theory of "stability" and of the stable family of probability distributions is that they are "attractors" for properly normed sums of independent and identically distributed random variables. Important special cases of stable distributions are the normal distribution, the Cauchy distribution and the LĂ©vy distribution. For details see stable distribution. (Wikipedia).

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Related pages

Geometric stable distribution | Univariate distribution | Indecomposable distribution | Location parameter | LĂ©vy distribution | Generalized extreme value distribution | Stable distribution | Scale parameter | Stability postulate | Extreme value theory | Probability distribution | Normal distribution | Convolution | Geometric distribution | Random variable | Cauchy distribution | Probability theory | Characteristic function (probability theory) | Infinite divisibility