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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. [ 1 ] [ 2 ] Of the four parameters defining the family, most attention has been focused on the stability parameter, α {\displaystyle \alpha } (see panel).
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. [ 2 ] Of the three parameters defining the distribution, the stability parameter α {\displaystyle \alpha } is most important.
The counterpart of the stable distribution in this case is the geometric stable distribution Max-stability : here the operation is to take the maximum of a number of random variables. The counterpart of the stable distribution in this case is the generalized extreme value distribution , and the theory for this case is dealt with as extreme ...
The Lévy skew alpha-stable distribution or stable distribution is a family of distributions often used to characterize financial data and critical behavior; the Cauchy distribution, Holtsmark distribution, Landau distribution, Lévy distribution and normal distribution are special cases. The Linnik distribution; The logistic distribution
The multivariate stable distribution defines linear relations between stable distribution marginals. [clarification needed] In the same way as for the univariate case, the distribution is defined in terms of its characteristic function. The multivariate stable distribution can also be thought as an extension of the multivariate normal ...
In spectroscopy, this distribution, with frequency as the dependent variable, is known as a van der Waals profile. [note 1] It is a special case of the inverse-gamma distribution. It is a stable distribution.
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Discrete-stable distributions have been used in numerous fields, in particular in scale-free networks such as the internet and social networks [2] or even semantic networks. [3] Both discrete and continuous classes of stable distribution have properties such as infinite divisibility, power law tails, and unimodality.