ABSTRACT
In this chapter we shall introduce several families of multivariate ℓ 1-norm symmetric distributions, which include the i.i.d. sample from exponential as its particular case. One family, denoted by n, consists of the scale mixture of the uniform distributions on the surface of the ℓ 1-norm unit sphere. Some of its properties will be discussed. Also described are a more general family Tn , of which the survival functions are functions of ℓ1-norm, and an important subset of Ln , namely L n,∞, which is constructed as a scale mixture of random vectors with i.i.d. exponential components. The relationships among these three families and some applications are given.
