Characteristic Functions of 1-Spherical and 1-Norm Symmetric Distributions and Their Applications

Kai Wang Ng and Guo-Liang Tian

Journal of Multivariate Analysis, 2001, vol. 76, issue 2, 192-213

Abstract: In this article we obtain the characteristic functions (c.f.'s) for 1-spherical distributions and simplify that of the 1-norm symmetric distributions to an 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 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.

Keywords: characteristic function; 1-norm symmetric distributions; 1-spherical distributions; order statistics; random weighting method; serial correlation (search for similar items in EconPapers)
Date: 2001
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