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On decompositional algorithms for uniform sampling from n-spheres and n-balls

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  • Harman, Radoslav
  • Lacko, Vladimír

Abstract

We describe a universal conditional distribution method for uniform sampling from n-spheres and n-balls, based on properties of a family of radially symmetric multivariate distributions. The method provides us with a unifying view on several known algorithms as well as enabling us to construct novel variants. We give a numerical comparison of the known and newly proposed algorithms for dimensions 5, 6 and 7.

Suggested Citation

  • Harman, Radoslav & Lacko, Vladimír, 2010. "On decompositional algorithms for uniform sampling from n-spheres and n-balls," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2297-2304, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2297-2304
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    References listed on IDEAS

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    1. 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.
    2. Yoshihiro Tashiro, 1977. "On methods for generating uniform random points on the surface of a sphere," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 295-300, December.
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    4. Hashorva, Enkelejd, 2008. "Conditional limiting distribution of beta-independent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 99(7), pages 1438-1459, August.
    5. Marsaglia, George & Tsang, Wai Wan, 2000. "The Ziggurat Method for Generating Random Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 5(i08).
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
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    Cited by:

    1. Yamazoe, Hiroya & Naito, Kanta, 2024. "Simultaneous confidence region of an embedded one-dimensional curve in multi-dimensional space," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    2. Abadir, Karim M. & Luati, Alessandra & Paruolo, Paolo, 2023. "GARCH density and functional forecasts," Journal of Econometrics, Elsevier, vol. 235(2), pages 470-483.
    3. Vladimír Lacko & Radoslav Harman, 2012. "A conditional distribution approach to uniform sampling on spheres and balls in L p spaces," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(7), pages 939-951, October.
    4. Alexandru Agapie, 2021. "Spherical Distributions Used in Evolutionary Algorithms," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    5. Wolf-Dieter Richter, 2019. "On (p1,…,pk)-spherical distributions," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-18, December.
    6. Planas Christophe & Rossi Alessandro, 2024. "The slice sampler and centrally symmetric distributions," Monte Carlo Methods and Applications, De Gruyter, vol. 30(3), pages 299-313.
    7. Jean-Thomas Camino & Christian Artigues & Laurent Houssin & Stéphane Mourgues, 2019. "Linearization of Euclidean norm dependent inequalities applied to multibeam satellites design," Computational Optimization and Applications, Springer, vol. 73(2), pages 679-705, June.
    8. Vic Patrangenaru & Peter Bubenik & Robert L. Paige & Daniel Osborne, 2019. "Challenges in Topological Object Data Analysis," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 244-271, February.
    9. Filippozzi, Rafaela & Gonçalves, Douglas S. & Santos, Luiz-Rafael, 2023. "First-order methods for the convex hull membership problem," European Journal of Operational Research, Elsevier, vol. 306(1), pages 17-33.

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