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

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  • Ng, Kai Wang
  • Tian, Guo-Liang

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.

Suggested Citation

  • Ng, Kai Wang & Tian, Guo-Liang, 2001. "Characteristic Functions of 1-Spherical and 1-Norm Symmetric Distributions and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 192-213, February.
    • Handle: RePEc:eee:jmvana:v:76:y:2001:i:2:p:192-213
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    References listed on IDEAS

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    1. Fang, Kai-Tai & Fang, Bi-Qi, 1988. "Some families of mutivariate symmetric distributions related to exponential distribution," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 109-122, January.
    2. Karlin, S. & Micchelli, C. A. & Rinott, Y., 1986. "Multivariate splines: A probabilistic perspective," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 69-90, October.
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