Generating Random Deviates
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.
KeywordsSuccess Probability Normal Deviate Standard Normal Deviate Random Deviate Adaptive Rejection Sampling
Unable to display preview. Download preview PDF.
- 9.Feller W (1971) An Introduction to Probability Theory and Its Applications, Volume 2, 2nd ed. Wiley, New YorkGoogle Scholar
- 12.Gilks WR (1992) Derivative-free adaptive rejection sampling for Gibbs sampling. In Bayesian Statistics 4, Bernardo JM, Berger JO, Dawid AP, Smith AFM, editors, Oxford University Press, Oxford, pp 641-649Google Scholar
- 18.Knuth D (1981) The Art of Computer Programming, 2: Seminumerical Algorithms, 2nd ed. Addison-Wesley, Reading MAGoogle Scholar
- 23.Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge University Press, CambridgeGoogle Scholar
- 29.von Neumann J (1951) Various techniques used in connection with random digits. Monte Carlo methods. Nat Bureau Standards 12:36-38Google Scholar