Probability Distributions
Dirk P. Kroese, Thomas Taimre, Zdravko I. Botev · Wiley series in probability and statistics · 2011
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 R2 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