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Stable distributions are a class of probability distributions allowing skewness and heavy tails (Rimmer and Nolan 2005). They are described by an index of stability (also known as a characteristic exponent) , and skewness parameter , a scale parameter , and a location parameter . Two possible parametrizations include
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(Rimmer and Nolan 2005). is most convenient for numerical computations, whereas is commonly used in economics.
REFERENCES:
Lévy, P. Calcul des probabilités. Paris: Gauthier-Villars, 1925.
Nolan, J. P. Stable Distributions: Models for Heavy Tailed Data. Boston, MA: Birkhäuser, 2005.
Nolan, J. P. "Stable MathLink Package." https://www.robustanalysis.com/.
Rimmer, R. H. and Nolan, J. P. "Stable Distributions in Mathematica." Mathematica J. 9, 776-789, 2005.
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