# 4. Probability Distributions

Published Online: 20 SEP 2011

DOI: 10.1002/9781118014967.ch4

Copyright © 2011 John Wiley & Sons, Inc.

Book Title

## Handbook of Monte Carlo Methods

Additional Information

#### How to Cite

Kroese, D. P., Taimre, T. and Botev, Z. I. (2011) Probability Distributions, in Handbook of Monte Carlo Methods, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118014967.ch4

#### Publication History

- Published Online: 20 SEP 2011
- Published Print: 28 FEB 2011

#### Book Series:

#### ISBN Information

Print ISBN: 9780470177938

Online ISBN: 9781118014967

- Summary
- Chapter
- References

### Keywords:

- continuous distributions;
- discrete distributions;
- Monte Carlo simulation;
- multivariate distribution;
- probability distribution;
- random variable generation

### Summary

This chapter lists the major discrete and continuous probability distributions used in Monte Carlo simulation, along with their main properties and specific algorithms for random variable generation. It also lists various multivariate distributions in alphabetical order. Many practically encountered multivariate singular continuous distributions involve absolutely continuous random vectors that are mapped to a lower-dimensional manifold. For example, the uniform distribution on the perimeter of a circle is singular with respect to the Lebesgue measure on R^{2} and so its two-dimensional pdf is zero. However, it is readily thought of as the distribution of a one-dimensional uniform random variable bent into a circle.

#### Controlled Vocabulary Terms

continuous distributions; discrete distributions; Monte Carlo methods; multivariate normal distribution; probability distribution; random variables