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

In this article, by employing the surface integral and other useful formulas related to multidimensional integrals, we obtain the characteristic functions (c.f.'s) for L 1-spherical and L 1-norm symmetric distributions. These c.f.'s can be used to derive the probability density functions (p.d.f.'s) of linear combinations of variables. We shall show that this gives a uniied 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 shown.