3. Random Variable Generation

  1. Dirk P. Kroese1,
  2. Thomas Taimre1 and
  3. Zdravko I. Botev2

Published Online: 20 SEP 2011

DOI: 10.1002/9781118014967.ch3

Handbook of Monte Carlo Methods

Handbook of Monte Carlo Methods

How to Cite

Kroese, D. P., Taimre, T. and Botev, Z. I. (2011) Random Variable Generation, in Handbook of Monte Carlo Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118014967.ch3

Author Information

  1. 1

    University of Queensland

  2. 2

    Université de Montréal

Publication History

  1. Published Online: 20 SEP 2011
  2. Published Print: 28 FEB 2011

ISBN Information

Print ISBN: 9780470177938

Online ISBN: 9781118014967



  • Monte Carlo simulation;
  • multivariate random variables;
  • one-dimensional random variables;
  • random variable generation methods;
  • random vectors


This chapter first presents various general methods for generating one-dimensional random variables and methods for generation of multivariate random variables. Then, it discusses generation methods for miscellaneous random objects, such as random vectors that are uniformly distributed over hyperspheres, ellipsoids, and Simplexes. All generation methods in the chapter are exact, in the sense that each generated random variable has exactly the required distribution (assuming the uniform number generation and computer arithmetic are exact). For an increasing number of Monte Carlo applications exact random variable generation is difficult or impossible to achieve, and approximate generation methods are called for, the most prominent being Markov chain Monte Carlo methods.

Controlled Vocabulary Terms

Monte Carlo methods; multivariate random variable; random variables