Characteristic Functions of L1-Spherical and L1-Norm Symmetric Distributions and Their Applications

In this article we obtain the characteristic functions (c.f.ʹs) for L1-spherical distributions and simplify that of the L1-norm symmetric distributions to an expression of a finite sum. These forms of c.f.ʹs can be used to derive the probability density functions (p.d.f.ʹs) of linear combinations of variables. We shall show that this gives a unified approach to the treatment of the linear function of i.i.d. random variables and their order statistics associated with double-exponential (i.e., Laplace), exponential, and uniform distributions. Some applications in reliability prediction, random weighting, and serial correlation are also shown.