Non-uniform Random Numbers - Continuous Distributions

Continuous Distributions

Generic methods for generating independent samples:

• Rejection sampling
• Inverse transform sampling
• Slice sampling
• Ziggurat algorithm, for monotonously decreasing density functions
• Convolution random number generator, not a sampling method in itself: it describes the use of arithmetics on top of one ore more existing sampling methods to generate more involved distributions.

Generic methods for generating correlated samples (often necessary for unusually-shaped or high-dimensional distributions):

• Markov chain Monte Carlo, the general principle
• Metropolis–Hastings algorithm
• Gibbs sampling
• Slice sampling
• Reversible-jump Markov chain Monte Carlo, when the number of dimensions is not fixed (e.g. when estimating a mixture model and simultaneously estimating the number of mixture components)
• Particle filters, when the observed data is connected in a Markov chain and should be processed sequentially

For generating a normal distribution:

• Box–Muller transform
• Marsaglia polar method

For generating a Poisson distribution:

• See Poisson distribution#Generating Poisson-distributed random variables