A conditional distribution approach to uniform sampling on spheres and balls in Lp spaces
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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.
KeywordsLp-norm n-sphere n-ball Uniform distribution p-generalized normal distribution Monte Carlo simulation Probabilistic robustness analysis
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