Statisticians rely on a combination of mathematical theory and statistical simulation to develop new methods. Because simulations are often conducted on a massive scale, it is crucial that they be efficiently executed. In the current chapter, we investigate techniques for producing random samples from univariate and multivariate distributions. These techniques stand behind every successful simulation and play a critical role in Monte Carlo integration. Exceptionally fast code for simulations almost always depends on using a lower-level computer language such as C or Fortran. This limitation forces the statistician to write custom software. Mastering techniques for generating random variables (or deviates in this context) is accordingly a useful survival skill.
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