Characteristic functions of \({\mathcal L}_1\)-spherical and \({\mathcal L}_1\)-norm symmetric distributions and their applications. (English) Zbl 0982.60005
Authors’ abstract: We obtain the characteristic functions (c.f.’s) for 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 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.
Reviewer: A.Ulanovskij (Khar’kov)
MSC:
| 60E10 | Characteristic functions; other transforms |
Keywords:
characteristic function; \(L_1\)-norm symmetric distributions; \(L_1\)-spherical distributions; order statistics; random weighting method; serial correlationReferences:
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