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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.

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H10 Multivariate distribution of statistics
Full Text: DOI
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