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Abstract:
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Four methods of sampling from any given distribution are considered: natural, inversive, rejective (especially, Lahiri's method), and geometric. In natural sampling, equally-likely sampling is done on a finite population that obeys the distribution approximately. Inversive sampling refers to choosing a random sample from a uniform distribution and applying the inverse of the cumulative distribution function (cdf), and to higher-dimensional generalizations. Rejective sampling refers to choosing a random sample from a product of independent uniform distributions and rejecting units that violate preimposed constraints. Lahiri's method, in particular, avoids computation of integrals and inverses. Geometric sampling exploits features of the distribution to transform the sampling into rejective and/or uniform sampling. One application is equal area/volume sampling from a surface/body.
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