Some families of multivariate symmetric distributions related to exponential distribution
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.
scale mixtures of the uniform distribution
scientific article; zbMATH DE number 4034872
scientific article