Some families of multivariate symmetric distributions related to exponential distribution (Q1097606)

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.