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

Vladimír Lacko () and Radoslav Harman ()

Metrika: International Journal for Theoretical and Applied Statistics, 2012, vol. 75, issue 7, 939-951

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. Copyright Springer-Verlag 2012

Keywords: L p -norm; n-sphere; n-ball; Uniform distribution; p-generalized normal distribution; Monte Carlo simulation; Probabilistic robustness analysis (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s00184-011-0360-x

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