Characteristic functions of L-1-spherical and L-1-norm symmetric distributions and their applications

In this article we obtain the characteristic functions (c.f's) for L-1-sphe rical distributions and simplify that of the L-1-norm symmetric distributio ns to all expression of a finite sum. These forms of c.f.'s can be used to derive the probability density functions (p.d.f's) of lineal combinations o f variables. We shall show that this gives a unified approach to the treatm ent of the linear function of i.i.d. random variables and their order stati stics associated with double-exponential (i.e., Laplace), exponential, and uniform distributions. Some applications in reliability prediction, random weighting, and serial correlation are also shown. (C) 2001 Academic Press.