Abstract
The main theorem of the paper states that every stable random vector with marginal skewness parameters different from ±1 can be turned into a sub-Gaussian random vector by using an appropriately tailored transformation in multidimensional space. The theorem is used to create a formula on probability density function of stable random vector and to perform a procedure of testing the stable distribution of multivariate data. A dataset collected from the Nasdaq stock market is used to illustrate the proposed procedure.
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