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

✍ Scribed by Kai Wang Ng; Guo-Liang Tian

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 176 KB
• Volume: 76
• Category: Article
• ISSN: 0047-259X
• DOI: 10.1006/jmva.2000.1910

✦ Synopsis

In this article we obtain the characteristic functions (c.f.'s) for L 1 -spherical distributions and simplify that of the L 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.