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A conditional distribution approach to uniform sampling on spheres and balls in Lp spaces

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Abstract

Liang and Ng (Metrika 68:83–98, 2008) proposed a componentwise conditional distribution method for L p -uniform sampling on L p -norm n-spheres. On the basis of properties of a special family of L p -norm spherical distributions we suggest a wide class of algorithms for sampling uniformly distributed points on n-spheres and n-balls in L p spaces, generalizing the approach of Harman and Lacko (J Multivar Anal 101:2297–2304, 2010), and including the method of Liang and Ng as a special case. We also present results of a numerical study proving that the choice of the best algorithm from the class significantly depends on the value of p.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48, Bratislava, Slovak Republic

    Vladimír Lacko & Radoslav Harman

Authors
  1. Vladimír Lacko
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  2. Radoslav Harman
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Correspondence to Vladimír Lacko.

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Lacko, V., Harman, R. A conditional distribution approach to uniform sampling on spheres and balls in Lp spaces. Metrika 75, 939–951 (2012). https://doi.org/10.1007/s00184-011-0360-x

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  • DOI: https://doi.org/10.1007/s00184-011-0360-x

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