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Uniform Distributions on Spheres in Finite DimensionalL[alpha]and Their Generalizations

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  • Szablowski, Pawel J.

Abstract

We characterize uniform distributions on spheres in n-dimensional spacesL[alpha]by certain Cauchy-like (n-1)-dimensional distributions of the quotients and derive some properties of mixtures of uniform distributions on such spheres, i.e.,[alpha]-spherical distributions. We feel that a simple Cauchy-like distribution is much simpler to deal with than the usual description of a uniform distribution on the sphere.

Suggested Citation

  • Szablowski, Pawel J., 1998. "Uniform Distributions on Spheres in Finite DimensionalL[alpha]and Their Generalizations," Journal of Multivariate Analysis, Elsevier, vol. 64(2), pages 103-117, February.
    • Handle: RePEc:eee:jmvana:v:64:y:1998:i:2:p:103-117
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    Cited by:

    1. Wolf-Dieter Richter, 2019. "On (p1,…,pk)-spherical distributions," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-18, December.
    2. Yang, Zhenhai & Pang, W.K. & Hou, S.H. & Leung, P.K., 2005. "On a combination method of VDR and patchwork for generating uniform random points on a unit sphere," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 23-36, July.
    3. Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.

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