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Some families of multivariate symmetric distributions related to exponential distribution. (English) Zbl 0635.62035
This paper introduces a family of multivariate symmetric distributions, which includes the one with i.i.d. exponential components as its special member. This family, denoted by $$F_ n$$, is defined as scale mixtures of the uniform distribution on the surface of the $$l_ 1$$ unit sphere and studied from several aspects such as distribution functions, probability density functions, marginal and conditional distributions and components’ independence.
A more general family $$T_ n$$ in which the survival functions are functions in $$l_ 1$$ norm and an important subset $$D_{n,\infty}$$ of scale mixtures of random vectors with i.i.d. exponential components are also discussed. The relationships among these three families and some applications are given.

##### MSC:
 62H05 Characterization and structure theory for multivariate probability distributions; copulas 62H10 Multivariate distribution of statistics
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