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Basic Concepts in Computational Physics pp 197–209Cite as

Random Sampling Methods

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Abstract

Random numbers sampled from non-uniform probability density functions are an important ingredient of stochastic methods. Here we discuss the direct sampling method, the inverse transformation method, the rejection method, and the method of probability mixing. All these methods are based on random numbers generated by pseudo random number generators which obey a uniform distribution. The quality of the generated random numbers is tested by means of the histogram method.

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Notes

  1. 1.

    This follows from the transformation of pdfs (see Chap. 14):

    $$\displaystyle{ f(y) =\int _{ 0}^{1}\!\mathrm{d}\,x_{ 1}\!\int _{0}^{1}\!\mathrm{d}\,x_{ 2}\,\delta [y -\mathrm{ max}(x_{1},x_{2})] = 2y. }$$
  2. 2.

    We make use of:

    $$\displaystyle{ \frac{\mathrm{d}} {\mathrm{d}x}\tan ^{-1}(x) = \frac{1} {1 + x^{2}}. }$$

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Authors and Affiliations

  1. Faculty of Physics, University of Duisburg-Essen, Duisburg, Germany

    Benjamin A. Stickler

  2. Institute of Theoretical and Computational Physics, Graz University of Technology, Graz, Austria

    Ewald Schachinger

Authors
  1. Benjamin A. Stickler
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  2. Ewald Schachinger
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© 2016 Springer International Publishing Switzerland

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Stickler, B.A., Schachinger, E. (2016). Random Sampling Methods. In: Basic Concepts in Computational Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-27265-8_13

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